The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  X  X  1  1 X^2  X  X X^2
 0  X  0  0  0  0  0  0 X^2  X X^2+X  X X^2 X^2+X X^2+X  X X^2+X  0 X^2
 0  0  X  0  0  0  X X^2+X X^2+X  X  X  0 X^2  X X^2+X  0  X X^2+X X^2
 0  0  0  X  0  X  X X^2+X  0  0 X^2 X^2  0 X^2+X  X X^2+X  0 X^2+X  0
 0  0  0  0  X  X  0 X^2+X  X X^2  X  X X^2+X  0  X  0 X^2+X X^2+X X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  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 X^2  0  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+243x^12+16x^13+698x^14+224x^15+1827x^16+1008x^17+3282x^18+1600x^19+3504x^20+1008x^21+1870x^22+224x^23+644x^24+16x^25+166x^26+53x^28

The gray image is a linear code over GF(2) with n=76, k=14 and d=24.
This code was found by Heurico 1.16 in 2.26 seconds.