The generator matrix

 1  1  1  1  X  X  1  1  1  1  1  1
 0  X  0 X^2+X  X  X  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  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+44x^4+40x^6+215x^8+600x^10+2296x^12+600x^14+215x^16+40x^18+44x^20+1x^24

The gray image is a linear code over GF(2) with n=48, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0157 seconds.