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+2 X+2 X^2  1  1  1 X^2+X  1  1  1  1  1 X^2+2  1  1  1 X+2  1 X^2+2 X^2+2 X+2  1  1 X^2  1 X^2+X X^2+X X^2+X+2  X X^2+2  1  1  1  1 X^2+X+2  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X  2 X^2  1 X^2 X+2  1  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^2+2  1  X  1  2 X^2+2  3  1 X^2+X+3 X+1  0 X^2+X+1  X  1  3  3 X+3  1  X  1 X^2  1  3  X  1 X^2+3  1  1  0 X^2 X+2 X^2+2 X+1 X^2+1 X+3  X X+3  1 X^2+3 X^2+X+2 X^2 X^2+2 X+2 X+1 X^2+X X^2+1  0 X^2+X X^2+X+2  3 X^2  1  1  1 X^2+X+2 X^2+X  1  2 X^2+X+2  1 X^2+1  X  0
 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+1  1 X^2+2  1 X^2+X X^2+X+2 X^2  X X^2+X+1 X^2+X+3 X^2 X+2  2 X^2+3  0 X^2+1 X^2+X+2 X^2+X+1  1  1  0 X^2+X+1 X^2+2 X^2+X+1  1 X+1  1  1  1  1  1 X^2 X+2  1  1 X+1  X X^2+X+1 X^2 X+2 X^2+X+3 X+2 X^2+X  1 X^2+2  X  2 X+3 X^2  0  X X^2 X^2  1 X^2+X+2 X^2+3  1 X^2+X+3 X^2+X+2  1  1 X^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+256x^93+658x^94+656x^95+700x^96+436x^97+292x^98+260x^99+232x^100+116x^101+194x^102+132x^103+56x^104+40x^105+38x^106+24x^107+3x^112+2x^114

The gray image is a code over GF(2) with n=776, k=12 and d=372.
This code was found by Heurico 1.16 in 0.641 seconds.