The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1
0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0
0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0
0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 0 0
0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0
0 0 0 0 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 0 0
0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0
0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0
0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0
0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0
generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+77x^8+168x^12+28x^14+128x^15+203x^16+384x^17+2160x^18+384x^19+56x^20+128x^21+232x^22+7x^24+112x^26+28x^30
The gray image is a linear code over GF(2) with n=72, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0492 seconds.