The generator matrix

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

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+76x^8+96x^9+232x^10+416x^11+406x^12+416x^13+240x^14+96x^15+59x^16+8x^18+2x^20

The gray image is a linear code over GF(2) with n=48, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0126 seconds.