The generator matrix

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

generates a code of length 97 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+99x^88+992x^89+2265x^90+4306x^91+5654x^92+8538x^93+9593x^94+13686x^95+13128x^96+14412x^97+14147x^98+13474x^99+10008x^100+8306x^101+4990x^102+3606x^103+1757x^104+1154x^105+403x^106+256x^107+116x^108+100x^109+22x^110+28x^111+18x^112+2x^113+3x^114+4x^115+1x^118+3x^120

The gray image is a code over GF(2) with n=776, k=17 and d=352.
This code was found by Heurico 1.16 in 242 seconds.