The generator matrix

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

generates a code of length 91 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+216x^84+850x^85+1714x^86+2362x^87+3057x^88+3334x^89+3467x^90+3710x^91+3401x^92+3222x^93+2565x^94+1826x^95+1334x^96+694x^97+429x^98+306x^99+120x^100+56x^101+54x^102+20x^103+14x^104+4x^105+10x^106+1x^108+1x^110

The gray image is a code over GF(2) with n=728, k=15 and d=336.
This code was found by Heurico 1.16 in 16 seconds.