The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1
0 X^3 0 0 0 X^3 0 0 X^3 X^3 0 0
0 0 X^3 0 0 X^3 0 X^3 X^3 0 0 0
0 0 0 X^3 0 X^3 X^3 X^3 0 0 0 0
0 0 0 0 X^3 X^3 X^3 0 0 X^3 0 0
generates a code of length 12 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+9x^8+236x^12+9x^16+1x^24
The gray image is a linear code over GF(2) with n=96, k=8 and d=32.
This code was found by Heurico 1.16 in -6.48e-008 seconds.