The generator matrix

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

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+66x^2+24x^3+496x^4+440x^5+990x^6+3632x^7+5086x^8+3632x^9+990x^10+440x^11+496x^12+24x^13+66x^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 0.109 seconds.