The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+312x^81+82x^82+100x^83+228x^84+608x^85+276x^86+72x^87+24x^88+296x^89+26x^90+20x^91+2x^104+1x^128

The gray image is a code over GF(2) with n=680, k=11 and d=324.
This code was found by Heurico 1.16 in 0.5 seconds.