The generator matrix

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

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+125x^8+204x^9+392x^10+168x^11+114x^12+12x^13+8x^14

The gray image is a code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in 1.05e-007 seconds.