The generator matrix

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

generates a code of length 98 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+212x^93+821x^94+1112x^95+1134x^96+914x^97+911x^98+700x^99+649x^100+458x^101+341x^102+262x^103+274x^104+160x^105+132x^106+70x^107+20x^108+16x^109+2x^110+1x^116+1x^120+1x^122

The gray image is a code over GF(2) with n=784, k=13 and d=372.
This code was found by Heurico 1.16 in 1.78 seconds.