The generator matrix

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

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+300x^91+831x^92+1338x^93+1675x^94+2164x^95+1727x^96+1804x^97+1413x^98+1312x^99+1222x^100+890x^101+534x^102+516x^103+255x^104+184x^105+103x^106+52x^107+42x^108+8x^109+2x^110+8x^111+1x^112+1x^116+1x^118

The gray image is a code over GF(2) with n=776, k=14 and d=364.
This code was found by Heurico 1.16 in 5.31 seconds.