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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+96x^89+140x^90+88x^91+88x^92+48x^93+20x^94+24x^95+2x^96+4x^100+1x^128

The gray image is a code over GF(2) with n=728, k=9 and d=356.
This code was found by Heurico 1.16 in 0.875 seconds.