The generator matrix

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

generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+14x^6+16x^7+82x^8+32x^9+80x^10+16x^11+12x^12+2x^14+1x^16

The gray image is a linear code over GF(2) with n=36, k=8 and d=12.
This code was found by Heurico 1.16 in 0.000417 seconds.