The generator matrix

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

generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+7x^6+52x^7+15x^8+40x^9+8x^10+4x^11+1x^14

The gray image is a linear code over GF(2) with n=32, k=7 and d=12.
This code was found by Heurico 1.16 in 0.000206 seconds.