The generator matrix

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

generates a code of length 93 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+206x^88+732x^89+1079x^90+1220x^91+1034x^92+814x^93+716x^94+620x^95+479x^96+436x^97+276x^98+204x^99+177x^100+98x^101+55x^102+28x^103+5x^104+8x^105+1x^106+1x^108+1x^110+1x^120

The gray image is a code over GF(2) with n=744, k=13 and d=352.
This code was found by Heurico 1.16 in 1.59 seconds.