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

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

Homogenous weight enumerator: w(x)=1x^0+68x^91+324x^92+242x^93+362x^94+396x^95+506x^96+436x^97+577x^98+384x^99+226x^100+142x^101+164x^102+92x^103+77x^104+24x^105+49x^106+4x^107+16x^108+4x^109+1x^112+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 1.58 seconds.