The generator matrix

 1  1  1  1  1  1  1  1  X  X X^2  1
 0  X  0  0  0  0  0 X^2 X^2+X X^2+X X^2 X^2+X
 0  0  X  0  0 X^2 X^2+X  X X^2+X  0  X X^2+X
 0  0  0  X  0 X^2+X X^2+X  X  0 X^2 X^2  0
 0  0  0  0  X  X X^2 X^2+X X^2+X  0 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+86x^8+200x^9+76x^10+480x^11+144x^12+784x^13+168x^14+32x^15+25x^16+40x^17+12x^18

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 0.0202 seconds.