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

generates a code of length 93 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+4x^92+94x^93+6x^94+12x^95+2x^96+6x^97+1x^100+1x^106+1x^110

The gray image is a code over GF(2) with n=744, k=7 and d=368.
This code was found by Heurico 1.16 in 0.578 seconds.