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  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  X  1  1  1  X  1  X  X
 0  2  0  2  0  2  0  2  0  2  2  0  2  0  0  2  0  2  0  2  0  2  0  2  0  2  0  2 2X 2X+2 2X 2X+2  0  2 2X 2X+2  0  2 2X 2X+2  0  2 2X 2X+2  0  2 2X 2X+2  0 2X  2 2X+2  0 2X  2 2X+2  0 2X  2 2X+2  0 2X  2 2X+2 2X 2X+2 2X 2X+2 2X 2X 2X+2 2X+2 2X  0  2 2X+2 2X+2 2X  0 2X+2 2X+2 2X 2X+2 2X  2 2X 2X+2 2X+2 2X+2  2  2 2X+2  2  2  2  2  2
 0  0 2X  0  0  0  0  0  0  0  0 2X  0 2X 2X  0  0  0  0  0  0  0  0  0 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0  0  0  0 2X 2X  0  0  0  0  0  0 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X  0 2X 2X 2X
 0  0  0 2X  0  0  0 2X  0  0  0  0 2X  0  0 2X  0  0  0  0  0  0  0  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0  0 2X  0 2X  0  0 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X 2X  0 2X  0  0  0 2X  0  0  0 2X
 0  0  0  0 2X  0  0  0 2X  0  0  0  0 2X 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X  0 2X  0  0 2X  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X  0  0  0  0  0  0  0 2X  0 2X 2X  0
 0  0  0  0  0 2X  0 2X  0  0 2X  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X 2X 2X 2X  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X 2X 2X 2X
 0  0  0  0  0  0 2X  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X  0 2X 2X 2X  0 2X 2X  0 2X 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+114x^92+16x^93+52x^94+64x^95+120x^96+1376x^97+56x^98+64x^99+90x^100+16x^101+20x^102+53x^104+4x^108+1x^112+1x^184

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 1.33 seconds.