The generator matrix

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

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+224x^83+990x^84+1472x^85+2523x^86+2712x^87+3589x^88+3550x^89+3730x^90+3244x^91+3538x^92+2304x^93+1913x^94+1076x^95+866x^96+466x^97+287x^98+124x^99+74x^100+48x^101+16x^102+8x^103+2x^104+3x^106+4x^107+4x^108

The gray image is a code over GF(2) with n=720, k=15 and d=332.
This code was found by Heurico 1.16 in 15.6 seconds.