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  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  0 X^2  0 X^2  0 X^2  0  X  X X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  X  X  X  X  X  X  2  2  2  2
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  2 X^2  2 X^2  2 X^2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  2 X^2  2 X^2  2 X^2 X^2+2 X^2+2 X^2+2 X^2+2 X^2  0  2 X^2 X^2  0  2 X^2  0  2  0 X^2+2  2 X^2  0 X^2+2  2 X^2  0 X^2+2  2 X^2  0 X^2+2  2 X^2 X^2+2 X^2 X^2+2 X^2 X^2+2 X^2 X^2+2 X^2  0  2  0  2  0  2  0  2 X^2 X^2 X^2 X^2  2  0  0  2  2  0  2 X^2 X^2 X^2 X^2
 0  0  2  0  0  2  2  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  2  2  2  0  0  0  2  2  2  0  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  0  0  2  2  0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  2  2  0  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  2  2  0  2  0  0  2  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  2  2  0  0  0  2  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+70x^92+128x^93+32x^94+15x^96+8x^100+2x^108

The gray image is a code over GF(2) with n=744, k=8 and d=368.
This code was found by Heurico 1.16 in 0.937 seconds.