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

generates a code of length 99 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+160x^96+64x^97+312x^98+128x^99+150x^100+64x^101+80x^102+28x^104+24x^106+10x^112+2x^116+1x^128

The gray image is a code over GF(2) with n=792, k=10 and d=384.
This code was found by Heurico 1.16 in 0.781 seconds.