The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+34x^14+132x^15+325x^16+568x^17+936x^18+1340x^19+1532x^20+1360x^21+908x^22+572x^23+306x^24+120x^25+40x^26+4x^27+12x^28+2x^30

The gray image is a linear code over GF(2) with n=80, k=13 and d=28.
This code was found by Heurico 1.16 in 0.46 seconds.