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

generates a code of length 85 over Z4[X]/(X^3+2,2X) 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.