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

generates a code of length 86 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+58x^84+416x^86+22x^88+12x^92+1x^112+2x^116

The gray image is a code over GF(2) with n=688, k=9 and d=336.
This code was found by Heurico 1.16 in 0.703 seconds.