The generator matrix

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

generates a code of length 10 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+456x^8+592x^9+2032x^10+544x^11+452x^12+16x^13+3x^16

The gray image is a code over GF(2) with n=80, k=12 and d=32.
This code was found by Heurico 1.16 in 153 seconds.