The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  2  1  1  1  2  1 X+2  1  1  1 X+2  1  1 X^2+2  1 X^2+X+2  1 X^2+2  1  1  1  1 X^2+2  1 X^2  1  1 X^2+X+2  1  1 X^2+X+2  1  1 X+2  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1 X^2+X  1  1  1  1  1  1  1  1  1 X^2+X X^2+2  2  0
 0  1  1 X^2 X+1  1  X X^2+X+1  1  X  1 X^2+X+1 X+1 X^2+1  1 X^2+X+2  1  0 X^2+X+2 X^2+X+3  1  3 X+2  1 X^2  1 X+1  1 X^2+1  0 X^2+X+1 X^2+2  1  2  1 X^2+3  3  1 X^2+X+2 X+3  1 X+2 X^2+1  1 X^2+2  3  1 X^2+X X^2+X+3  1  3 X^2+3 X^2+3  3 X+3 X^2+3 X+3 X+3 X^2+X+3 X^2+X+3 X^2+3 X^2+1 X^2+X+3 X+3 X^2+2 X^2+2 X^2+X+3  1 X+3 X^2+X+1 X^2+X+3  1  X X^2+3 X^2+3 X+1 X+3  1  1 X^2+X+2 X^2  1  1  1  1
 0  0  X X+2  2 X+2 X+2  X X^2+2 X^2 X+2 X^2+2 X^2+X X^2+X+2 X^2  0  0 X^2+2 X+2  2 X^2+X+2  0 X^2+X X^2+X+2  2 X+2  X X^2 X^2 X^2+X+2 X^2+X+2 X^2+2  2 X^2+X X^2+X X^2+2 X^2+X  0 X^2+X+2 X^2 X^2+X  0  2 X^2 X+2  X X+2 X^2+2 X^2+2 X^2+X+2 X^2+2  X X+2 X^2 X^2+2 X^2+X  X  2 X^2+X+2  0  2  0 X+2 X^2+X+2 X^2+X X^2+X+2  X X^2+X X+2  2 X^2+X  X X^2+X+2 X^2 X^2+X+2  0 X^2+X  2 X+2  X  0 X^2+X+2  0 X^2+2 X^2+X+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+370x^82+338x^83+289x^84+104x^85+281x^86+316x^87+316x^88+8x^89+4x^90+2x^91+1x^92+16x^94+1x^126+1x^128

The gray image is a code over GF(2) with n=680, k=11 and d=328.
This code was found by Heurico 1.16 in 124 seconds.