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

generates a code of length 97 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+90x^91+238x^92+322x^93+328x^94+428x^95+478x^96+490x^97+500x^98+320x^99+322x^100+262x^101+66x^102+76x^103+92x^104+38x^105+14x^107+20x^108+8x^109+2x^110+1x^160

The gray image is a code over GF(2) with n=776, k=12 and d=364.
This code was found by Heurico 1.16 in 1.55 seconds.