The generator matrix

 1  0  1  1  1 3X+2  2 X+2  X  1
 0  1 X+1 X+2 2X+3  1  1  1 2X  0
 0  0 2X+2 2X+2  0  0 2X 2X+2 2X+2  0
 0  0  0 2X  0 2X 2X  0  0  0
 0  0  0  0 2X 2X  0 2X  0  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+24x^6+96x^7+233x^8+1052x^9+1273x^10+1068x^11+242x^12+84x^13+14x^14+4x^15+4x^16+1x^18

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 0.016 seconds.