The generator matrix

 1  1  1  1  1  1  2  X  1  1  2  X
 0  X  0  X  2 X+2  X X^2+X+2 X^2 X^2+X+2 X^2+2  0
 0  0  X  X X^2 X^2+X X+2 X^2+2  X X^2+X+2  X X^2+X

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+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.