The generator matrix

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

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+31x^6+66x^7+305x^8+896x^9+1506x^10+892x^11+298x^12+64x^13+31x^14+2x^15+4x^16

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.