The generator matrix

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

generates a code of length 91 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+94x^85+157x^86+368x^87+293x^88+388x^89+551x^90+550x^91+538x^92+386x^93+199x^94+228x^95+102x^96+96x^97+53x^98+54x^99+25x^100+12x^101+1x^156

The gray image is a code over GF(2) with n=728, k=12 and d=340.
This code was found by Heurico 1.16 in 1.3 seconds.