The generator matrix

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

generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+55x^8+32x^9+128x^10+224x^11+144x^12+224x^13+128x^14+32x^15+55x^16+1x^24

The gray image is a linear code over GF(2) with n=48, k=10 and d=16.
This code was found by Heurico 1.16 in 0.00439 seconds.