The generator matrix

 1  0  1  1  1  0  1  1  X  1  1 X^2+X  X  X  0 X^2 X^2  0  0  1
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+X X^2+1  1 X^2  X  1  1  X  1  1  0
 0  0  X X^2+X  0 X^2+X  X X^2+X  X X^2  0  0  X  X  0  X  X  0  0  0
 0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0
 0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 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+55x^12+62x^13+137x^14+316x^15+553x^16+1556x^17+1343x^18+3164x^19+1942x^20+3296x^21+1402x^22+1364x^23+502x^24+460x^25+174x^26+20x^27+19x^28+2x^29+13x^30+3x^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 1.39 seconds.