The generator matrix

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

generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+46x^4+52x^5+142x^6+240x^7+830x^8+1464x^9+844x^10+240x^11+142x^12+52x^13+38x^14+5x^16

The gray image is a linear code over GF(2) with n=36, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0135 seconds.