The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X X 1 X 1 1 1 1 X 1 1 X 1 X 1 0 1 1 X 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X 2X 2X X X 2X 0 X X X X X 0 2X X X X X 0 X 0 X 2X 2X X 0 2X 0 X 0 2X 2X 2X 2X 0 2X X 2X 2X 0 X X 2X 0 0 0 0 0 X 0 0 2X X X 2X X X 0 X 2X X X 2X X 0 0 2X 0 X X X 2X X X 2X
0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X 0 X X 2X 2X 0 X X 0 2X 2X 0 2X 0 X 0 0 X 2X 0 2X X 0 X X X X 0 2X 2X 2X 0 X X 0 2X 0 0 X 2X 0 0 X 2X X X 2X 2X X X X X 0 X 2X X X 0 2X 2X 0 X X 2X 0 X 0 2X 0 0 2X X 0 0 X 0 X X
0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 0 X X 0 2X X 0 X 0 0 X 0 2X 2X X 0 X X 0 2X X 0 X X 2X 0 2X 2X 2X X 2X 0 0 0 X 0 0 2X X 0 X 0 X 2X 2X X 2X 2X 2X 0 X 2X 0 X 0 0 2X 0 2X X 2X 0 2X 0 2X 2X 0 0 2X X X 2X 2X 2X
0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X 2X X 0 0 2X 2X 0 2X 0 0 X X 2X X 0 X 0 2X 2X 0 0 2X X X 2X X X 0 X 2X 2X 2X X X X X X 2X 0 2X X 0 0 2X X 2X 2X 0 0 0 2X X 0 2X 0 0 2X 2X X 0 0 X 0 X 2X 0 X 0 2X X 2X 0 0 2X
0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 0 2X X X 0 X X 0 0 0 0 X 2X 2X 2X X X X X X 2X 2X 2X 2X 2X 0 2X 2X 0 2X 2X X X 2X 0 2X 0 0 0 X 2X 2X 0 2X 0 0 0 0 0 X 2X 2X 0 0 X 2X 2X 2X 0 X 2X 2X 0 0 2X 2X X 2X 2X 2X 0 0 X 2X
0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X X X X 0 2X 0 0 0 X 2X 0 2X X 0 0 0 2X 0 0 X 2X 0 2X 0 X 2X X 2X 2X X 0 X X 2X X 0 2X X X X X 0 X X 0 X X X 2X 0 2X 0 X 2X 0 0 X 2X X 0 2X 2X 0 2X 0 X 0 2X 0 X X X X
generates a code of length 96 over Z3[X]/(X^2) who´s minimum homogenous weight is 174.
Homogenous weight enumerator: w(x)=1x^0+116x^174+220x^177+264x^180+352x^183+676x^186+1088x^189+1336x^192+1106x^195+656x^198+274x^201+92x^204+76x^207+88x^210+82x^213+32x^216+40x^219+30x^222+12x^225+8x^228+8x^231+2x^234+2x^261
The gray image is a linear code over GF(3) with n=288, k=8 and d=174.
This code was found by Heurico 1.16 in 77.1 seconds.