The generator matrix

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

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+20x^2+100x^4+428x^6+2998x^8+428x^10+100x^12+20x^14+1x^16

The gray image is a linear code over GF(2) with n=32, k=12 and d=4.
This code was found by Heurico 1.16 in 0.00755 seconds.