The generator matrix

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

generates a code of length 97 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+162x^92+934x^93+957x^94+1234x^95+914x^96+938x^97+557x^98+800x^99+449x^100+414x^101+207x^102+238x^103+165x^104+90x^105+29x^106+64x^107+10x^108+24x^109+2x^112+1x^116+2x^122

The gray image is a code over GF(2) with n=776, k=13 and d=368.
This code was found by Heurico 1.16 in 1.56 seconds.