The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+20x^6+104x^7+231x^8+1048x^9+1288x^10+1048x^11+231x^12+104x^13+20x^14+1x^20

The gray image is a code over GF(2) with n=80, k=12 and d=24.
This code was found by Heurico 1.16 in 0.031 seconds.