The generator matrix

 1  1  1  1  1  1  1  1 X^3  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^3  0
 0  0 X^3 X^3 X^3  0  0 X^3  0  0

generates a code of length 10 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+11x^8+124x^9+11x^10+88x^11+4x^12+12x^13+4x^14+1x^18

The gray image is a linear code over GF(2) with n=80, k=8 and d=32.
This code was found by Heurico 1.16 in 1.05e-007 seconds.