The generator matrix

 1  1  1  1  1  1  1  1  X  X  1  1 X^2 X^2  1  X X^2  1  1
 0  X  0  0  0  X X^2+X  X X^2  0  X  0  X  X  X X^2+X  X  0  0
 0  0  X  0  X  X X^2+X  0  0  X  X  X X^2+X X^2  0  X X^2+X X^2  0
 0  0  0  X  X  0 X^2+X  X  X  X  0 X^2+X X^2 X^2+X X^2+X X^2+X  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 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+104x^12+78x^13+219x^14+234x^15+727x^16+422x^17+2015x^18+562x^19+2014x^20+458x^21+760x^22+222x^23+216x^24+66x^25+72x^26+6x^27+10x^28+5x^30+1x^34

The gray image is a linear code over GF(2) with n=76, k=13 and d=24.
This code was found by Heurico 1.16 in 0.612 seconds.