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

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+93x^92+384x^93+31x^96+3x^124

The gray image is a code over GF(2) with n=744, k=9 and d=368.
This code was found by Heurico 1.16 in 0.938 seconds.