The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+54x^13+174x^14+356x^15+561x^16+954x^17+1308x^18+1372x^19+1299x^20+954x^21+614x^22+348x^23+122x^24+54x^25+16x^26+4x^27+1x^36

The gray image is a linear code over GF(2) with n=76, k=13 and d=26.
This code was found by Heurico 1.16 in 0.633 seconds.