The generator matrix

 1  0  0  0  1  1  1  1
 0  1  0  0  1  X  0  1
 0  0  1  0  1 X+1 X+1  0
 0  0  0  1  X  1  0  1
 0  0  0  0 X^2  0 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+71x^4+196x^5+914x^6+1584x^7+2639x^8+1624x^9+908x^10+176x^11+73x^12+4x^13+2x^14

The gray image is a linear code over GF(2) with n=32, k=13 and d=8.
This code was found by Heurico 1.11 in -6.48e-008 seconds.