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

generates a code of length 97 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 94.

Homogenous weight enumerator: w(x)=1x^0+88x^94+190x^96+512x^97+176x^98+56x^102+1x^192

The gray image is a code over GF(2) with n=776, k=10 and d=376.
This code was found by Heurico 1.16 in 48.1 seconds.