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

generates a code of length 98 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+258x^93+772x^94+1016x^95+1172x^96+1052x^97+822x^98+760x^99+572x^100+526x^101+354x^102+240x^103+200x^104+176x^105+150x^106+64x^107+45x^108+4x^109+5x^110+1x^112+1x^116+1x^126

The gray image is a code over GF(2) with n=784, k=13 and d=372.
This code was found by Heurico 1.16 in 1.59 seconds.