The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+122x^12+322x^14+64x^15+1217x^16+576x^17+2488x^18+1408x^19+3969x^20+1408x^21+2508x^22+576x^23+1238x^24+64x^25+312x^26+100x^28+2x^30+8x^32+1x^36

The gray image is a linear code over GF(2) with n=80, k=14 and d=24.
This code was found by Heurico 1.16 in 1.81 seconds.