The generator matrix
1 1 1 1 1 1 1 1 X X X X
0 2 0 0 0 2 2 2 0 0 2 0
0 0 2 0 2 2 2 0 0 2 2 0
0 0 0 2 2 0 2 2 2 2 0 0
generates a code of length 12 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+8x^10+108x^12+8x^14+3x^16
The gray image is a code over GF(2) with n=96, k=7 and d=40.
This code was found by Heurico 1.16 in -6.48e-008 seconds.