The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  1  1  1  1 X^2  X X^2 X^2  1
 0  X  0  0  0  0  0  0 X^2 X^2 X^2+X X^2+X X^2+X  X X^2+X X^2 X^2  X X^2  0
 0  0  X  0  0  0  0  0  0  X  0 X^2+X X^2 X^2+X X^2+X  X X^2 X^2+X  X X^2
 0  0  0  X  0  0 X^2 X^2+X  X X^2+X X^2+X  0 X^2+X X^2 X^2  0 X^2+X  X  X  0
 0  0  0  0  X  0 X^2+X X^2+X  X  0 X^2 X^2+X X^2  0 X^2+X X^2+X X^2+X  X X^2+X X^2
 0  0  0  0  0  X  X X^2  X  X  X  X X^2+X X^2+X X^2 X^2 X^2+X  0  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+42x^13+114x^14+212x^15+326x^16+556x^17+896x^18+1170x^19+1393x^20+1344x^21+974x^22+562x^23+279x^24+164x^25+92x^26+38x^27+15x^28+6x^29+4x^30+2x^31+2x^32

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 0.835 seconds.