The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+136x^80+798x^81+2144x^82+4210x^83+6694x^84+10766x^85+15091x^86+20730x^87+25335x^88+29418x^89+30786x^90+29726x^91+26565x^92+21238x^93+14799x^94+10382x^95+5981x^96+3716x^97+1930x^98+852x^99+485x^100+204x^101+78x^102+32x^103+15x^104+14x^105+2x^106+4x^107+2x^108+4x^109+2x^110+2x^112+2x^113

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 845 seconds.