The generator matrix

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

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+84x^4+320x^5+800x^6+1728x^7+2326x^8+1728x^9+800x^10+320x^11+84x^12+1x^16

The gray image is a linear code over GF(2) with n=32, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0356 seconds.