The generator matrix

 1  0  1  1  1 X+2  1  1 3X+2  1  1 3X+2 X+2 2X+2  1  1 2X+2  1  1  1  1 3X  1  1 3X  1  1  2  1  1  1  X  1  1 2X  0  1  1  1  X  1  1  1  2  1  1  1  1  1 2X  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X X+2 2X+2  1  1  1 X+2 2X  1
 0  1  1 2X+2 X+1  1  X 2X+1  1 3X+2 3X+1  1  1  1 2X+2 2X+3  1 X+3 3X+2 2X  3  1 3X 3X+3  1  0 3X+1  1 3X 2X+1 2X  1  3 3X+2  1  1  2  1  X  1 3X+3 X+1 X+2  1  3  2  2 X+3  1  1  0 2X 2X X+2  2 X+2  X  0 2X+2  X 3X 3X+2 2X+3  0  X X+1 2X+2 3X+1 3X+2 X+1 X+3  2 2X+1 3X 3X+2  0  1  1  1  0  1 X+3  1  1  0
 0  0  X 3X 2X 3X 3X 2X  0  0  X 3X+2  2 2X+2 X+2  2  X 3X+2 2X+2 2X+2 3X+2 3X+2 X+2  2  X 3X+2 2X+2 3X+2  2 X+2 3X 2X+2  X 3X+2 3X  2  2  2  0  0 2X 3X+2  X  0 2X  0 3X+2 3X 2X+2 3X+2  X  0  2 X+2 2X 3X 2X+2 3X 2X+2 2X 3X+2  X  0  X  2 X+2 3X+2  2  2 3X 2X  X 3X  0 2X X+2 2X  X X+2  2  0  X X+2  X  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+88x^81+249x^82+412x^83+201x^84+254x^85+185x^86+304x^87+184x^88+106x^89+36x^90+12x^91+6x^92+4x^93+4x^95+1x^118+1x^126

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 0.516 seconds.