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

generates a code of length 98 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+126x^92+128x^93+347x^94+326x^95+463x^96+486x^97+552x^98+464x^99+424x^100+248x^101+170x^102+78x^103+128x^104+30x^105+63x^106+28x^107+26x^108+4x^109+2x^110+1x^114+1x^166

The gray image is a code over GF(2) with n=784, k=12 and d=368.
This code was found by Heurico 1.16 in 1.59 seconds.