The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+22x^14+34x^15+65x^16+194x^17+48x^18+316x^19+40x^20+188x^21+48x^22+34x^23+22x^24+2x^25+8x^26+2x^30

The gray image is a linear code over GF(2) with n=76, k=10 and d=28.
This code was found by Heurico 1.16 in 0.0155 seconds.