The generator matrix

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

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+76x^12+16x^13+74x^14+160x^15+173x^16+752x^17+188x^18+1216x^19+188x^20+752x^21+173x^22+160x^23+74x^24+16x^25+76x^26+1x^38

The gray image is a linear code over GF(2) with n=76, k=12 and d=24.
This code was found by Heurico 1.16 in 0.131 seconds.