The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+56x^13+261x^14+532x^15+1176x^16+2372x^17+3801x^18+5120x^19+5847x^20+5488x^21+3891x^22+2228x^23+1203x^24+516x^25+171x^26+56x^27+29x^28+16x^29+4x^30

The gray image is a linear code over GF(2) with n=80, k=15 and d=26.
This code was found by Heurico 1.16 in 6.81 seconds.