The generator matrix

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

generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+57x^10+32x^11+77x^12+32x^13+54x^14+1x^16+1x^18+1x^20

The gray image is a linear code over GF(2) with n=48, k=8 and d=20.
This code was found by Heurico 1.16 in 0.0018 seconds.