The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+118x^80+292x^81+490x^82+640x^83+448x^84+476x^85+328x^86+408x^87+375x^88+276x^89+86x^90+72x^91+52x^92+12x^93+2x^94+8x^96+2x^100+6x^102+2x^104+1x^116+1x^124

The gray image is a code over GF(2) with n=680, k=12 and d=320.
This code was found by Heurico 1.16 in 0.953 seconds.