The generator matrix

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

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+29x^80+92x^81+63x^82+212x^83+732x^84+104x^85+444x^86+84x^87+98x^88+80x^89+36x^90+56x^91+4x^92+12x^93+1x^162

The gray image is a code over GF(2) with n=680, k=11 and d=320.
This code was found by Heurico 1.16 in 1.03 seconds.