The generator matrix

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

generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+34x^4+116x^5+397x^6+880x^7+1197x^8+968x^9+370x^10+80x^11+48x^12+4x^13+1x^14

The gray image is a linear code over GF(2) with n=32, k=12 and d=8.
This code was found by Heurico 1.16 in 0.00998 seconds.