The generator matrix
1 1 1 1 1 1 X 0 1 1 X 0 1 1 1 1 X 1 1
0 X 0 X^2+X 0 X^2+X X X X^2 X^2+X X^2+X X 0 0 0 0 X^2 0 0
0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0
0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0
0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0
0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0
0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0
0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2
generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+59x^12+16x^14+217x^16+256x^17+160x^18+512x^19+366x^20+256x^21+80x^22+102x^24+23x^28
The gray image is a linear code over GF(2) with n=76, k=11 and d=24.
This code was found by Heurico 1.16 in 0.0392 seconds.