The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+83x^88+992x^89+2409x^90+3940x^91+6096x^92+8216x^93+9996x^94+12822x^95+13474x^96+15474x^97+13367x^98+13346x^99+10322x^100+7776x^101+5387x^102+3304x^103+1837x^104+1162x^105+554x^106+214x^107+162x^108+68x^109+45x^110+6x^111+9x^112+8x^113+2x^114

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 245 seconds.