The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+82x^14+160x^15+433x^16+440x^17+1094x^18+944x^19+1865x^20+912x^21+1182x^22+480x^23+374x^24+120x^25+74x^26+16x^27+14x^28+1x^36

The gray image is a linear code over GF(2) with n=80, k=13 and d=28.
This code was found by Heurico 1.16 in 0.694 seconds.