The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+612x^82+1900x^83+4325x^84+7040x^85+11020x^86+15016x^87+21280x^88+24936x^89+29576x^90+29804x^91+30099x^92+26612x^93+21100x^94+15112x^95+10786x^96+6056x^97+3632x^98+1604x^99+919x^100+340x^101+210x^102+80x^103+42x^104+8x^105+18x^106+4x^107+1x^108+6x^110+3x^112+2x^114

The gray image is a code over GF(2) with n=728, k=18 and d=328.
This code was found by Heurico 1.16 in 857 seconds.