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

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+183x^84+66x^88+5x^92+1x^120

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 1.97 seconds.