The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+310x^82+68x^83+160x^84+160x^85+644x^86+264x^87+74x^88+324x^90+20x^91+20x^92+2x^106+1x^128

The gray image is a code over GF(2) with n=688, k=11 and d=328.
This code was found by Heurico 1.16 in 0.515 seconds.