The generator matrix

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

generates a code of length 97 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+94x^92+176x^94+144x^95+403x^96+480x^97+386x^98+144x^99+117x^100+52x^102+28x^104+10x^106+12x^108+1x^180

The gray image is a code over GF(2) with n=776, k=11 and d=368.
This code was found by Heurico 1.16 in 1.36 seconds.