The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  0  X  1  1  X  X  X  1
 0  X  0  X  0  0  X X^2+X  0 X^2  X X^2+X  X X^2+X  X X^2  0  X  0  0
 0  0  X  X  0 X^2+X  X  0 X^2  X  X  0  0 X^2  X X^2 X^2+X X^2+X X^2+X  0
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 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+35x^14+48x^15+103x^16+128x^17+217x^18+336x^19+313x^20+336x^21+231x^22+128x^23+83x^24+48x^25+27x^26+11x^28+2x^30+1x^32

The gray image is a linear code over GF(2) with n=80, k=11 and d=28.
This code was found by Heurico 1.16 in 0.052 seconds.