The generator matrix

 1  0  1  1  1  0  X  X
 0  1  1  0 X+1  1 X^2 X^2
 0  0  X  0  X  0  0 X^2
 0  0  0  X  X X^2+X  X X^2+X
 0  0  0  0 X^2  0 X^2  0
 0  0  0  0  0 X^2 X^2  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+83x^4+128x^5+422x^6+896x^7+1031x^8+896x^9+436x^10+128x^11+69x^12+6x^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 0.00944 seconds.