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

generates a code of length 97 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+7x^96+100x^97+6x^98+10x^101+1x^106+2x^109+1x^122

The gray image is a code over GF(2) with n=776, k=7 and d=384.
This code was found by Heurico 1.16 in 1.09 seconds.