The generator matrix

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

generates a code of length 90 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+590x^82+2004x^83+3764x^84+5956x^85+8082x^86+10788x^87+12857x^88+14584x^89+14662x^90+14596x^91+12639x^92+10716x^93+7932x^94+5388x^95+3134x^96+1812x^97+852x^98+360x^99+173x^100+80x^101+50x^102+16x^103+24x^104+4x^105+6x^106+2x^114

The gray image is a code over GF(2) with n=720, k=17 and d=328.
This code was found by Heurico 1.16 in 209 seconds.