The generator matrix

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

generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+248x^8+288x^9+1096x^10+1248x^11+2398x^12+1248x^13+1184x^14+288x^15+167x^16+24x^18+2x^20

The gray image is a linear code over GF(2) with n=48, k=13 and d=16.
This code was found by Heurico 1.16 in 9.61 seconds.