The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2X+2) 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 5.34e-008 seconds.