The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+394x^82+288x^83+347x^84+296x^85+198x^86+104x^87+241x^88+56x^89+54x^90+24x^91+32x^92+2x^94+1x^96+8x^98+1x^116+1x^120

The gray image is a code over GF(2) with n=680, k=11 and d=328.
This code was found by Heurico 1.16 in 97.8 seconds.