The generator matrix

 1  0  0  0  1  1  1  X  X  1  1  1  X  0  1 X^2  X X^2  1
 0  1  0  0  X  1  1  1  0 X^2+X+1  X X^2  1  1 X^2+1  1  1  1  0
 0  0  1  0 X+1  1  X X+1  1  1  0 X+1  1  X  0 X+1 X+1  1  0
 0  0  0  1  1 X^2+X X+1  1  1 X+1  1  X  0  1  0 X^2+1 X+1 X+1  0
 0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 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+69x^12+244x^13+382x^14+1412x^15+2218x^16+3940x^17+5540x^18+5188x^19+5502x^20+3932x^21+2208x^22+1452x^23+396x^24+204x^25+60x^26+12x^27+5x^28+2x^30+1x^32

The gray image is a linear code over GF(2) with n=76, k=15 and d=24.
This code was found by Heurico 1.16 in 4.9 seconds.