The generator matrix

 1  0  0  1  1  1 2X  1  1  0  1  1  2 X+2  1 3X+2 3X  1 2X  1  1  1 3X+2 X+2  1 3X  1  1  1  X  1 2X+2  1 X+2  1 2X  0  1  1  1  1 2X+2 3X  1 2X+2  1  X  1  1 3X 2X 2X  1 3X+2  1  1  1  2  X 3X+2  1  1  1  1 X+2  1  1 3X  1  1  0  2 3X+2  1 2X+2 2X  1  1  1  1 2X+2  1 X+2  1  1
 0  1  0 2X 2X+3  3  1  X 3X 3X 3X+3 X+3  1  1 2X+2  1 3X+2 X+1  1  2  3  X  1  1 2X+1  0  3 X+1 X+2  1 3X  1 2X+3 3X X+1 2X+2  1 2X+3 2X+2 3X 2X  1  1  1  1 X+3  1 3X+3 3X+2  1 X+2  1 X+1 2X+2  0 3X+1 2X+1  1  1  1 X+2 3X+2 2X+1 2X+3  1  2 2X+2  1  2  2  1 3X+2 X+2 2X  1  1  X  2 X+3  1 2X+2 3X+2 2X  1  2
 0  0  1 3X+1 X+1 2X 3X+1 3X 2X+3  1  3  X X+2 2X+1 3X X+2  1 X+3  3 2X+1 X+2  2  2 3X+3 2X+2  1  3 X+2 2X+1 X+1 3X+3  X  1  1  0  1  1  X 3X+3 3X+2 2X+3 2X 2X X+3  3  0  1  1 3X+1 3X+2  1 3X+3 2X+1  1  2 3X+1  0  2  3 2X 3X+2  2  3 X+3 3X 3X+2  0  2 2X+3 X+1  X  1  1  X 3X+2 2X+2  0 2X+2 3X+3 X+1  1 X+2  1 3X+1  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+172x^81+732x^82+620x^83+664x^84+480x^85+324x^86+264x^87+302x^88+100x^89+180x^90+124x^91+61x^92+32x^93+36x^94+2x^96+1x^100+1x^112

The gray image is a code over GF(2) with n=680, k=12 and d=324.
This code was found by Heurico 1.16 in 0.484 seconds.