The generator matrix
1 1 1 1 1 1 1 1 X X 1 1
0 X 0 X^2+X 0 X^2 X^2+X X^2+X 0 X^2 0 0
0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0
0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0
0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0
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+22x^8+32x^10+148x^12+32x^14+17x^16+4x^20
The gray image is a linear code over GF(2) with n=48, k=8 and d=16.
This code was found by Heurico 1.16 in 0.000915 seconds.