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

generates a code of length 85 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+84x^83+75x^84+220x^85+32x^86+76x^87+14x^88+4x^89+3x^92+1x^104+2x^108

The gray image is a code over GF(2) with n=680, k=9 and d=332.
This code was found by Heurico 1.16 in 72.8 seconds.