The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+826x^84+1898x^85+3348x^86+4222x^87+5922x^88+6632x^89+7168x^90+7070x^91+7054x^92+5766x^93+5350x^94+3810x^95+3053x^96+1672x^97+917x^98+402x^99+188x^100+108x^101+72x^102+32x^103+20x^104+4x^105+1x^106

The gray image is a code over GF(2) with n=728, k=16 and d=336.
This code was found by Heurico 1.16 in 53.8 seconds.