The generator matrix

 1  1  1  1  1  1  1  1  X  1  X  X  1  1  1  1  1  1  X  1
 0  X  0  X  0  0  X X^2+X X^2  0 X^2+X  X  X X^2+X  X X^2  X  0  0  X
 0  0  X  X  0 X^2+X  X  0  X X^2  0  X  X  0 X^2+X X^2+X  X  0  0 X^2+X
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2
 0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 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+22x^13+61x^14+112x^15+136x^16+120x^17+579x^18+240x^19+1522x^20+276x^21+584x^22+144x^23+126x^24+88x^25+52x^26+16x^27+6x^28+6x^29+3x^30+1x^32+1x^34

The gray image is a linear code over GF(2) with n=80, k=12 and d=26.
This code was found by Heurico 1.16 in 3.14 seconds.