The generator matrix

 1  0  1  1  1  0  X  1
 0  1  1  0 X+1  1 X^2  0
 0  0  X X^2+X  0 X^2+X  X  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  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+55x^4+48x^5+246x^6+464x^7+415x^8+464x^9+260x^10+48x^11+41x^12+6x^14

The gray image is a linear code over GF(2) with n=32, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00277 seconds.