The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+126x^81+346x^82+462x^83+478x^84+522x^85+482x^86+428x^87+434x^88+318x^89+219x^90+128x^91+61x^92+50x^93+18x^94+4x^95+1x^96+8x^97+4x^98+2x^106+2x^107+1x^122+1x^124

The gray image is a code over GF(2) with n=688, k=12 and d=324.
This code was found by Heurico 1.16 in 0.984 seconds.