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

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

Homogenous weight enumerator: w(x)=1x^0+32x^93+14x^94+6x^95+1x^96+5x^98+2x^99+2x^100+1x^106

The gray image is a code over GF(2) with n=744, k=6 and d=372.
This code was found by Heurico 1.16 in 0.594 seconds.