The generator matrix

 1  1  1  1  1  1  1  1
 0  X  0  0  0  X  0  0
 0  0  X  0  0  X  0  0
 0  0  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

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+48x^2+428x^4+1936x^6+11558x^8+1936x^10+428x^12+48x^14+1x^16

The gray image is a linear code over GF(2) with n=32, k=14 and d=4.
This code was found by Heurico 1.16 in 0.11 seconds.