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

generates a code of length 93 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+68x^86+70x^87+199x^88+164x^89+357x^90+254x^91+830x^92+350x^93+792x^94+262x^95+305x^96+88x^97+149x^98+44x^99+66x^100+30x^101+38x^102+8x^103+3x^104+8x^105+1x^106+2x^107+4x^108+2x^110+1x^162

The gray image is a code over GF(2) with n=744, k=12 and d=344.
This code was found by Heurico 1.16 in 1.8 seconds.