The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+192x^15+395x^16+520x^17+551x^18+740x^19+634x^20+560x^21+298x^22+152x^23+32x^24+8x^25+7x^26+4x^27+2x^28

The gray image is a linear code over GF(2) with n=76, k=12 and d=30.
This code was found by Heurico 1.16 in 0.126 seconds.