The generator matrix

 1  0  0  0  1  1  1 3X+2  1 3X+2  1  X  1 2X+2  1 3X+2  1 3X  1 3X  1  1  1  2  2  0  1  1 2X  1  1  1  1  2  2  1  1  1  X 3X+2  1  1 3X  1  1 3X+2 X+2  1  2  1  X  X 3X+2 X+2  1 2X  1 X+2  1  1  0 2X 2X X+2 3X  1 3X+2  1 2X+2  1  1 3X 3X  1  0  1  1  X 2X  1  1  1  1  0  1 3X+2  1  1  2  1  1  X  X
 0  1  0  0 2X  3 3X+1  1 2X+2 2X+2 2X+2  1 3X+3  1  1 2X+2  0  0 3X+3  1 X+1 X+3 2X+1  0  1  1 3X+2 3X  1  2  0 2X 2X+3  1  2 2X 3X  3  1  1 3X+2 3X+3 3X X+2 X+1 2X  1 X+1  X 3X 2X+2  1 X+2  1 3X+1  1 3X  1 3X X+3 3X+2  X  1 3X  1 2X+2  1 3X+3 X+2 X+2 3X  1  1  1 X+2 3X+2 X+1 X+2  1 X+3 X+3 3X+3  0  1  3  1 3X 3X+2  1 X+3  0  1  1
 0  0  1  0  2 2X 2X+2 2X+2  1  1 X+3 X+3  3 X+1 3X+1  2  2  1 2X+2  2 2X+2 3X+3  3  1 2X+3 X+2 X+3 3X+1  3 X+2 2X+1  X 3X 3X  1 3X+2 2X+3  1 2X+2 2X+3 X+2 3X+3  1  0 3X  1 X+3 X+3  2 3X+1  1  X 2X+2 2X+3  0 X+1  3 2X 3X 3X+2  1  X 2X+2 X+2 3X+3 2X+1 X+2  3  1 X+1 2X+2 3X+2 2X X+2  1  2  1 3X 3X 3X+2  1  1  0  1 X+1 3X X+3 3X+1 X+1  X 3X X+2 2X
 0  0  0  1 3X+3 X+3 2X X+1 3X+1 X+3  0 2X+1 3X+2 3X 2X+1  1  3 2X+1  X  X  1  1  0  X 2X+2  3 3X+2  3  1 3X+2  2 X+3  3  0  3 2X+2 3X+3 3X+3  3 2X+1 X+2 2X X+1 X+1 2X+2  2 2X X+3  1 3X+1 X+2 2X+2  1 X+2  X 3X+1 2X+3 2X+2  0 2X+1 X+2  1 3X+2  1 X+2 2X+3  X  2 X+1  0  0  3 X+1  2  3 2X+3 2X+3  1 X+1 2X+3 3X+1 2X+1 3X+2 3X+1 2X+3 3X+1  2 3X X+3 3X+3  3  0 3X+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+864x^86+2060x^87+3196x^88+4592x^89+5584x^90+6608x^91+7033x^92+7024x^93+7114x^94+6128x^95+4873x^96+3960x^97+2780x^98+1828x^99+974x^100+432x^101+242x^102+108x^103+70x^104+24x^105+24x^106+4x^107+13x^108

The gray image is a code over GF(2) with n=744, k=16 and d=344.
This code was found by Heurico 1.16 in 237 seconds.