The generator matrix

 1  1  1  1  X  1  1  1  1  X  1  1
 0  X  0  0  X  0  X X^2+X  0  0  0  0
 0  0  X  0  X  X  X X^2+X X^2+X  0  0  0
 0  0  0  X  X  X  0 X^2+X  0  0  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+304x^6+1031x^8+1616x^10+2048x^11+6232x^12+2048x^13+1616x^14+1031x^16+304x^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 0.243 seconds.