The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+18x^3+71x^4+202x^5+726x^6+1828x^7+2495x^8+1828x^9+740x^10+202x^11+57x^12+18x^13+6x^14

The gray image is a linear code over GF(2) with n=32, k=13 and d=6.
This code was found by Heurico 1.16 in 0.038 seconds.