The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+232x^84+848x^85+1450x^86+1534x^87+1776x^88+1950x^89+1846x^90+1646x^91+1542x^92+1134x^93+820x^94+600x^95+453x^96+254x^97+150x^98+70x^99+35x^100+18x^101+12x^102+6x^103+4x^105+1x^108+2x^110

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 4.81 seconds.