The generator matrix

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

generates a code of length 97 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+119x^88+1018x^89+2326x^90+3998x^91+6165x^92+8188x^93+10094x^94+12456x^95+14259x^96+13986x^97+14222x^98+13344x^99+10016x^100+7912x^101+5790x^102+3210x^103+1864x^104+1092x^105+536x^106+270x^107+111x^108+56x^109+14x^110+2x^111+8x^112+4x^113+8x^114+2x^118+1x^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 228 seconds.