The generator matrix

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

generates a code of length 96 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+322x^93+337x^94+308x^95+324x^96+214x^97+251x^98+134x^99+42x^100+80x^101+2x^102+22x^103+1x^106+8x^109+1x^118+1x^152

The gray image is a code over GF(2) with n=768, k=11 and d=372.
This code was found by Heurico 1.16 in 0.75 seconds.