The generator matrix
1 0 1 1 1 X^2 1 1 1 X^2 1 X X^2 1 1 1 1 0 X 1
0 1 1 0 X+1 1 1 0 X^2 1 X+1 1 1 X^2+1 X^2+X X+1 X 1 X^2 0
0 0 X 0 0 X^2 0 X^2+X X^2+X X^2+X X^2+X X^2 X^2+X X^2 0 X X^2+X X^2+X X 0
0 0 0 X X^2 X X^2+X X^2+X X^2 X^2 X X^2+X X^2+X X^2 0 X^2 X^2 X 0 0
generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+46x^16+146x^17+51x^18+240x^19+58x^20+260x^21+64x^22+96x^23+23x^24+26x^25+11x^26+2x^30
The gray image is a linear code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in 0.0137 seconds.