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

generates a code of length 96 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+176x^93+90x^94+176x^95+202x^96+144x^97+84x^98+112x^99+2x^100+2x^102+32x^103+1x^120+1x^124+1x^132

The gray image is a code over GF(2) with n=768, k=10 and d=372.
This code was found by Heurico 1.16 in 1.5 seconds.