The generator matrix

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

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+52x^14+118x^16+128x^17+192x^18+384x^19+280x^20+384x^21+232x^22+128x^23+104x^24+32x^26+8x^28+4x^30+1x^32

The gray image is a linear code over GF(2) with n=80, k=11 and d=28.
This code was found by Heurico 1.16 in 0.0927 seconds.