The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+76x^5+601x^6+3492x^7+16644x^8+54264x^9+111935x^10+54344x^11+16660x^12+3452x^13+583x^14+84x^15+7x^16+1x^18

The gray image is a code over GF(2) with n=80, k=18 and d=20.
This code was found by Heurico 1.16 in 24.3 seconds.