The generator matrix

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

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+52x^13+107x^14+202x^15+301x^16+572x^17+912x^18+1200x^19+1452x^20+1236x^21+934x^22+612x^23+282x^24+180x^25+88x^26+32x^27+12x^28+8x^29+7x^30+2x^31

The gray image is a linear code over GF(2) with n=80, k=13 and d=26.
This code was found by Heurico 1.16 in 0.774 seconds.