The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+67x^80+786x^81+1991x^82+3938x^83+6150x^84+10884x^85+16116x^86+20692x^87+25161x^88+29868x^89+30285x^90+30204x^91+26012x^92+21276x^93+15839x^94+10184x^95+5735x^96+3732x^97+1761x^98+846x^99+336x^100+148x^101+51x^102+36x^103+20x^104+10x^105+1x^106+4x^107+2x^108+2x^110+2x^112+2x^116+2x^118

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 813 seconds.