The generator matrix

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

generates a code of length 90 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+102x^80+736x^81+2143x^82+4218x^83+7216x^84+10322x^85+15686x^86+20478x^87+24901x^88+28918x^89+31433x^90+29518x^91+26251x^92+21128x^93+15466x^94+10356x^95+6397x^96+3328x^97+1996x^98+812x^99+385x^100+162x^101+82x^102+34x^103+25x^104+26x^105+10x^106+8x^107+2x^108+4x^109

The gray image is a code over GF(2) with n=720, k=18 and d=320.
This code was found by Heurico 1.16 in 781 seconds.