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.