The generator matrix
1 1 1 1 1 1 X 1 1 X X X
0 2X+2 0 2X+2 0 2X+2 2X+2 2X 2 2X+2 2X+2 2X+2
0 0 2X 0 0 0 0 2X 0 0 2X 2X
0 0 0 2X 0 0 0 0 2X 0 2X 2X
0 0 0 0 2X 0 0 2X 0 2X 0 2X
0 0 0 0 0 2X 0 0 2X 2X 0 2X
0 0 0 0 0 0 2X 0 0 2X 2X 2X
generates a code of length 12 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+87x^8+128x^10+1616x^12+128x^14+87x^16+1x^24
The gray image is a code over GF(2) with n=96, k=11 and d=32.
This code was found by Heurico 1.16 in 0.015 seconds.