The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+26x^10+70x^12+106x^14+256x^16+540x^18+2048x^19+580x^20+300x^22+92x^24+42x^26+22x^28+10x^30+3x^32

The gray image is a linear code over GF(2) with n=76, k=12 and d=20.
This code was found by Heurico 1.16 in 0.0749 seconds.