The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+84x^9+85x^10+84x^11+1x^14+1x^16

The gray image is a code over GF(2) with n=80, k=8 and d=36.
This code was found by Heurico 1.16 in 0 seconds.