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  X  1  X  X  X  X  X  X  1  1  1  1  1  1  X  X  X  X  1  X  X  X  1  1  1  1  1  2  2  2  2  2  2  2  X  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1
 0 2X  0  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0  0 2X  0 2X 2X 2X  0  0  0  0 2X 2X  0
 0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0 2X 2X 2X 2X  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0 2X 2X  0  0
 0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0  0  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+34x^84+72x^85+4x^86+6x^87+1x^88+3x^90+4x^92+2x^103+1x^106

The gray image is a code over GF(2) with n=680, k=7 and d=336.
This code was found by Heurico 1.16 in 0.406 seconds.