The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  1  0  1  X  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X^2+X X+1  1  0  0 X+1 X+1
 0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0
 0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 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+103x^12+88x^14+128x^15+662x^16+896x^17+2232x^18+2048x^19+4083x^20+2048x^21+2184x^22+896x^23+704x^24+128x^25+104x^26+69x^28+9x^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 1.27 seconds.