The generator matrix

 1  0  0  0  0  1  1  1  1 X^2  1 X^2 X^2+X  1  1  1  1 X^2+X X^2+X X^2
 0  1  0  0  0  0 X^2  0  0 X^2  1  1  1 X^2+1 X^2+X X^2+X+1  X  1  1 X^2+X
 0  0  1  0  0  0  1 X^2 X+1  1 X+1 X^2+X  1 X^2  1 X^2+1  1 X+1 X^2+X  0
 0  0  0  1  0  1  1  X  0 X^2+1 X^2+1 X+1  0 X^2  X  X X^2+1 X^2  X  1
 0  0  0  0  1  1  X X+1 X+1 X+1 X^2+X+1 X+1 X+1 X^2 X^2+X X+1 X^2+1 X^2+X  1 X^2+X+1
 0  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  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+431x^14+804x^15+3237x^16+3516x^17+9328x^18+7860x^19+14700x^20+8140x^21+9974x^22+3564x^23+2770x^24+628x^25+488x^26+60x^27+28x^28+4x^29+3x^30

The gray image is a linear code over GF(2) with n=80, k=16 and d=28.
This code was found by Heurico 1.13 in 10.3 seconds.