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

generates a code of length 93 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+202x^90+324x^92+356x^94+56x^96+82x^98+2x^120+1x^128

The gray image is a code over GF(2) with n=744, k=10 and d=360.
This code was found by Heurico 1.16 in 1.11 seconds.