The generator matrix

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

generates a code of length 96 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+268x^92+642x^93+648x^94+622x^95+454x^96+364x^97+337x^98+194x^99+162x^100+134x^101+85x^102+92x^103+16x^104+32x^105+33x^106+9x^108+1x^114+2x^120

The gray image is a code over GF(2) with n=768, k=12 and d=368.
This code was found by Heurico 1.16 in 0.625 seconds.