The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+142x^15+366x^16+616x^17+922x^18+1286x^19+1523x^20+1312x^21+940x^22+602x^23+313x^24+120x^25+26x^26+18x^27+5x^28

The gray image is a linear code over GF(2) with n=80, k=13 and d=30.
This code was found by Heurico 1.16 in 5.15 seconds.