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.