The generator matrix

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

generates a code of length 97 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+206x^93+175x^94+208x^95+306x^96+328x^97+235x^98+208x^99+140x^100+194x^101+36x^102+8x^103+1x^120+1x^126+1x^138

The gray image is a code over GF(2) with n=776, k=11 and d=372.
This code was found by Heurico 1.16 in 1.2 seconds.