The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+101x^12+292x^16+256x^18+2775x^20+256x^22+340x^24+67x^28+7x^32+1x^36

The gray image is a linear code over GF(2) with n=80, k=12 and d=24.
This code was found by Heurico 1.16 in 0.157 seconds.