The generator matrix

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

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+69x^4+154x^6+594x^8+512x^9+2280x^10+1536x^11+6050x^12+1536x^13+2412x^14+512x^15+429x^16+264x^18+25x^20+10x^22

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 0.25 seconds.