The generator matrix

 1  1  1  1  1  1  X  0  1  1  X  1  1  X  X  1  1  1  1  1
 0  X  0 X^2+X  0 X^2+X  X  X  0 X^2+X  X  0 X^2+X X^2+X X^2+X  0  0  0  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2
 0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2
 0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+42x^10+116x^12+226x^14+128x^15+730x^16+640x^17+1780x^18+3328x^19+2392x^20+3328x^21+1780x^22+640x^23+760x^24+128x^25+226x^26+84x^28+42x^30+13x^32

The gray image is a linear code over GF(2) with n=80, k=14 and d=20.
This code was found by Heurico 1.16 in 0.993 seconds.