The generator matrix

 1  1  1  1  1  1  X  0  1  1  X 2X
 0  X  0 3X+2 2X+2 X+2 3X+2  X  2  X X+2  X
 0  0  2  0 2X+2 2X+2 2X 2X  0 2X+2 2X+2  2
 0  0  0 2X 2X  0  0 2X  0  0 2X 2X

generates a code of length 12 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+182x^10+128x^11+412x^12+128x^13+164x^14+3x^16+6x^18

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 0.016 seconds.