The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+12x^84+216x^85+12x^86+2x^88+8x^89+2x^90+1x^96+2x^98

The gray image is a code over GF(2) with n=680, k=8 and d=336.
This code was found by Heurico 1.16 in 0.25 seconds.