The generator matrix

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

generates a code of length 98 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+102x^92+212x^93+333x^94+350x^95+404x^96+402x^97+593x^98+482x^99+368x^100+272x^101+231x^102+130x^103+77x^104+42x^105+27x^106+30x^107+20x^108+14x^110+4x^112+1x^122+1x^162

The gray image is a code over GF(2) with n=784, k=12 and d=368.
This code was found by Heurico 1.16 in 1.61 seconds.