The generator matrix

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

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+90x^87+213x^88+308x^89+370x^90+416x^91+453x^92+502x^93+539x^94+442x^95+255x^96+116x^97+113x^98+104x^99+81x^100+50x^101+9x^102+4x^103+12x^104+16x^105+1x^106+1x^152

The gray image is a code over GF(2) with n=744, k=12 and d=348.
This code was found by Heurico 1.16 in 1.36 seconds.