The generator matrix

 1  1  1  1  1  1  X  1
 0  X  0  0  0  X X^2  0
 0  0  X  0  X  X  X  0
 0  0  0  X  X X^2 X^2  0
 0  0  0  0 X^2 X^2  0  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+39x^4+32x^5+54x^6+224x^7+319x^8+224x^9+68x^10+32x^11+25x^12+6x^14

The gray image is a linear code over GF(2) with n=32, k=10 and d=8.
This code was found by Heurico 1.16 in 0.00135 seconds.