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

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

Homogenous weight enumerator: w(x)=1x^0+11x^82+28x^83+52x^84+336x^85+50x^86+12x^87+10x^88+8x^89+1x^90+1x^104+2x^118

The gray image is a code over GF(2) with n=680, k=9 and d=328.
This code was found by Heurico 1.16 in 0.672 seconds.