The generator matrix

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

generates a code of length 97 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+188x^87+971x^88+2356x^89+4794x^90+7928x^91+11095x^92+15116x^93+20622x^94+24836x^95+28458x^96+29168x^97+28598x^98+25216x^99+21103x^100+15500x^101+11250x^102+6828x^103+3940x^104+2216x^105+914x^106+568x^107+230x^108+88x^109+82x^110+36x^111+22x^112+4x^113+8x^114+4x^116+2x^118+2x^122

The gray image is a code over GF(2) with n=776, k=18 and d=348.
This code was found by Heurico 1.16 in 861 seconds.