The generator matrix

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

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+236x^85+948x^86+1146x^87+1846x^88+1732x^89+1855x^90+1776x^91+1927x^92+1202x^93+1319x^94+822x^95+701x^96+270x^97+261x^98+168x^99+74x^100+40x^101+21x^102+24x^103+1x^104+6x^105+4x^106+1x^108+2x^109+1x^112

The gray image is a code over GF(2) with n=728, k=14 and d=340.
This code was found by Heurico 1.16 in 4.94 seconds.