The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1
 0 X^2  0  0  0  0  0  0  0 X^2  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+36x^4+135x^8+1704x^12+135x^16+36x^20+1x^24

The gray image is a linear code over GF(2) with n=48, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00528 seconds.