The generator matrix

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

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+82x^10+320x^11+220x^12+320x^13+76x^14+3x^16+2x^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.