The generator matrix
1 1 1 1 1 1 1 X 1 1
0 X^3 0 0 0 0 0 X^3 X^3 0
0 0 X^3 0 0 0 X^3 X^3 X^3 0
0 0 0 X^3 0 0 X^3 0 0 X^3
0 0 0 0 X^3 0 X^3 0 X^3 X^3
0 0 0 0 0 X^3 X^3 X^3 0 0
generates a code of length 10 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+9x^6+16x^8+32x^9+399x^10+32x^11+12x^12+7x^14+3x^16+1x^18
The gray image is a linear code over GF(2) with n=80, k=9 and d=24.
This code was found by Heurico 1.16 in 0.016 seconds.