The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X  1  1 3X+2  1  2  1  1  1  1  1 2X  X  1  1  1  1 2X+2 X+2  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  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+1  1  2 X+3  1 2X+3  1 X+2 3X 2X 3X+1  1  1  1 2X+2  X 3X+3  3  1  1  0 X+2  2  X 2X 3X+2 2X+2  X 2X X+2 2X+2 3X 2X X+2 2X+2  X X+1 2X+3 3X+1  3 3X+3  1 3X+3  1 3X+1  3 3X+3 2X+1 3X+1  3 X+3  1  0 3X+2 3X+2  0  0
 0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X  0 2X  0 2X  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X  0  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0  0 2X  0 2X 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X 2X 2X  0

generates a code of length 85 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+30x^82+128x^83+192x^84+320x^85+192x^86+128x^87+28x^88+2x^90+1x^96+1x^104+1x^136

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 0.422 seconds.