The generator matrix

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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+144x^81+827x^82+1982x^83+4615x^84+6440x^85+11259x^86+14664x^87+21693x^88+23874x^89+30898x^90+29636x^91+30377x^92+24320x^93+22283x^94+14640x^95+11257x^96+5888x^97+3820x^98+1836x^99+843x^100+362x^101+306x^102+84x^103+31x^104+26x^105+11x^106+6x^107+13x^108+2x^109+4x^110+2x^112

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 791 seconds.