The generator matrix

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

generates a code of length 91 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+98x^82+874x^83+2155x^84+4060x^85+5417x^86+8402x^87+9979x^88+12988x^89+13873x^90+15676x^91+13929x^92+13160x^93+10382x^94+8224x^95+4834x^96+3344x^97+1692x^98+1126x^99+496x^100+162x^101+89x^102+62x^103+28x^104+10x^105+1x^106+4x^107+2x^109+2x^112+2x^113

The gray image is a code over GF(2) with n=728, k=17 and d=328.
This code was found by Heurico 1.16 in 223 seconds.