The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X
0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2
0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2
0 0 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 0 0 X^2 X^2
0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2
0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0
0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2
0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0
0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2
0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0
0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2
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+126x^8+532x^12+2404x^16+10240x^18+2392x^20+602x^24+84x^28+3x^32
The gray image is a linear code over GF(2) with n=72, k=14 and d=16.
This code was found by Heurico 1.16 in 0.812 seconds.