The generator matrix

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

generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+69x^2+156x^3+614x^4+940x^5+2539x^6+6072x^7+11986x^8+6072x^9+2539x^10+940x^11+614x^12+156x^13+69x^14+1x^16

The gray image is a linear code over GF(2) with n=32, k=15 and d=4.
This code was found by Heurico 1.16 in 0.252 seconds.