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

generates a code of length 92 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+232x^87+796x^88+1100x^89+1014x^90+1016x^91+803x^92+816x^93+749x^94+476x^95+310x^96+310x^97+217x^98+126x^99+100x^100+62x^101+33x^102+22x^103+4x^104+2x^106+1x^108+1x^112+1x^114

The gray image is a code over GF(2) with n=736, k=13 and d=348.
This code was found by Heurico 1.16 in 1.58 seconds.