The generator matrix

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

generates a code of length 91 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+92x^81+699x^82+2096x^83+3798x^84+6892x^85+10501x^86+15650x^87+20901x^88+26042x^89+29119x^90+31170x^91+28888x^92+26336x^93+20787x^94+15264x^95+10303x^96+6910x^97+3498x^98+1646x^99+788x^100+428x^101+190x^102+52x^103+53x^104+18x^105+4x^106+8x^107+2x^108+2x^110+2x^111+2x^112+2x^113

The gray image is a code over GF(2) with n=728, k=18 and d=324.
This code was found by Heurico 1.16 in 847 seconds.