The generator matrix

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

generates a code of length 93 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+269x^86+866x^87+1693x^88+2266x^89+3342x^90+3036x^91+3755x^92+3326x^93+3650x^94+2968x^95+2785x^96+1700x^97+1330x^98+668x^99+504x^100+278x^101+141x^102+74x^103+50x^104+42x^105+12x^106+4x^107+3x^108+4x^109+1x^112

The gray image is a code over GF(2) with n=744, k=15 and d=344.
This code was found by Heurico 1.16 in 16.9 seconds.