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

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+40x^83+12x^84+398x^85+14x^86+8x^87+17x^88+6x^90+2x^92+1x^106+2x^117

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.