The generator matrix

 1  1  1  1  X  X  X  1
 0  X  0 X^2+X  X  X  0  0
 0  0 X^2  0  0  0 X^2  0
 0  0  0 X^2  0  0 X^2  0
 0  0  0  0 X^2  0 X^2  0
 0  0  0  0  0 X^2 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+23x^4+16x^5+54x^6+48x^7+223x^8+48x^9+68x^10+16x^11+9x^12+6x^14

The gray image is a linear code over GF(2) with n=32, k=9 and d=8.
This code was found by Heurico 1.16 in 0.000483 seconds.