The generator matrix

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

generates a code of length 90 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+796x^83+1856x^84+3318x^85+4476x^86+5690x^87+6367x^88+7452x^89+6956x^90+7000x^91+6214x^92+5486x^93+3882x^94+2596x^95+1650x^96+996x^97+380x^98+224x^99+64x^100+76x^101+22x^102+14x^103+16x^105+4x^106

The gray image is a code over GF(2) with n=720, k=16 and d=332.
This code was found by Heurico 1.16 in 53.1 seconds.