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

generates a code of length 97 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 94.

Homogenous weight enumerator: w(x)=1x^0+384x^94+264x^95+484x^96+32x^97+320x^98+176x^99+254x^100+32x^101+56x^102+8x^103+26x^104+1x^108+8x^110+1x^124+1x^144

The gray image is a code over GF(2) with n=776, k=11 and d=376.
This code was found by Heurico 1.16 in 42.6 seconds.