The generator matrix

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

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+259x^8+232x^9+1186x^10+1280x^11+2183x^12+1360x^13+1308x^14+192x^15+148x^16+8x^17+34x^18+1x^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 2.63 seconds.