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

generates a code of length 85 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+20x^87+4x^88+4x^89+2x^90+1x^92

The gray image is a code over GF(2) with n=680, k=5 and d=348.
This code was found by Heurico 1.16 in 0.422 seconds.