The generator matrix

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

generates a code of length 98 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 95.

Homogenous weight enumerator: w(x)=1x^0+328x^95+326x^96+400x^97+196x^98+280x^99+174x^100+184x^101+44x^102+64x^103+24x^104+8x^105+8x^107+1x^108+8x^111+1x^112+1x^156

The gray image is a code over GF(2) with n=784, k=11 and d=380.
This code was found by Heurico 1.16 in 25.8 seconds.