The generator matrix

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

generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+76x^4+264x^6+855x^8+128x^9+2424x^10+1920x^11+5048x^12+1920x^13+2424x^14+128x^15+855x^16+264x^18+76x^20+1x^24

The gray image is a linear code over GF(2) with n=48, k=14 and d=8.
This code was found by Heurico 1.16 in 0.176 seconds.