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

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+48x^82+328x^83+100x^84+120x^85+62x^86+312x^87+10x^88+8x^89+32x^90+1x^96+1x^102+1x^134

The gray image is a code over GF(2) with n=680, k=10 and d=328.
This code was found by Heurico 1.16 in 0.937 seconds.