The generator matrix

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

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+71x^12+76x^13+234x^14+300x^15+712x^16+1092x^17+1773x^18+2604x^19+2566x^20+2652x^21+1852x^22+1124x^23+700x^24+268x^25+218x^26+68x^27+43x^28+8x^29+18x^30+3x^32+1x^34

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 2.13 seconds.