The generator matrix

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

generates a code of length 90 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+233x^84+828x^85+1305x^86+1652x^87+1818x^88+2116x^89+1723x^90+1736x^91+1423x^92+1098x^93+817x^94+624x^95+436x^96+284x^97+134x^98+80x^99+32x^100+24x^101+4x^102+4x^103+6x^104+1x^106+2x^109+1x^112+2x^116

The gray image is a code over GF(2) with n=720, k=14 and d=336.
This code was found by Heurico 1.16 in 4.56 seconds.