The generator matrix
1 0 0 0 1 1 1 X^2 1 X^2 1 X 1 1 1 1 0 1 1 1
0 1 0 0 0 1 1 1 X^2+X+1 1 X^2 X^2+X X^2+1 X^2+X+1 X 0 X^2 0 X X^2
0 0 1 0 1 1 X X+1 X X+1 0 1 0 X+1 X+1 X^2 1 X^2+1 X^2+X 0
0 0 0 1 1 0 X+1 1 X^2+X 0 X+1 1 X+1 X^2+1 X X X^2+1 X^2+X+1 X 0
0 0 0 0 X X^2 0 X^2 X X X^2+X 0 X 0 X^2 X X^2+X X^2+X 0 X
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+81x^14+258x^15+655x^16+1240x^17+1751x^18+2580x^19+3140x^20+2682x^21+1919x^22+1162x^23+548x^24+236x^25+89x^26+32x^27+8x^28+2x^29
The gray image is a linear code over GF(2) with n=80, k=14 and d=28.
This code was found by Heurico 1.13 in 0.704 seconds.