The generator matrix

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

generates a code of length 93 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+300x^87+774x^88+1380x^89+1669x^90+2040x^91+1630x^92+1916x^93+1423x^94+1664x^95+1068x^96+878x^97+627x^98+456x^99+254x^100+128x^101+77x^102+28x^103+17x^104+34x^105+4x^106+8x^107+6x^108+2x^112

The gray image is a code over GF(2) with n=744, k=14 and d=348.
This code was found by Heurico 1.16 in 5.24 seconds.