The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+164x^81+654x^82+732x^83+656x^84+464x^85+380x^86+268x^87+248x^88+132x^89+87x^90+120x^91+116x^92+32x^93+29x^94+8x^95+1x^96+1x^98+2x^100+1x^102

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 0.453 seconds.