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

generates a code of length 92 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+224x^86+120x^87+324x^88+248x^89+500x^90+408x^91+592x^92+408x^93+474x^94+232x^95+190x^96+104x^97+114x^98+8x^99+97x^100+8x^101+22x^102+8x^104+10x^106+3x^108+1x^152

The gray image is a code over GF(2) with n=736, k=12 and d=344.
This code was found by Heurico 1.16 in 2.39 seconds.