The generator matrix
1 1 1 1 1 1 2 X 1 1 2X X
0 X 0 X 2X 3X X 3X+2 2 3X+2 2X+2 2X
0 0 X X 2 X+2 3X 2X+2 X 3X+2 X X
generates a code of length 12 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+148x^10+208x^11+360x^12+160x^13+108x^14+16x^15+23x^16
The gray image is a code over GF(2) with n=96, k=10 and d=40.
This code was found by Heurico 1.16 in 0.015 seconds.