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  X  X  1  1  1  1  1  1  X  X  X  X  X  X  X  1  1  1  1  1  1  X  1  X  1  X  1  X  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  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  2  2  0  2  2  2  0  2  2  2  2  0  0  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  0  0  2  2  2
 0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  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  0  2  0  0  0  2  2  2  2  2  0  0  0  2  0  2  0  2  0  2  2  0  0  0  2  2  0  2
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  2  2  2  2  2  2  2  2  0  0  2  0  0  2  0  0  0  0  0  2  2  0  0  0  0  2  2  0  0  0  2  2  0  0  2
 0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  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  0  2  2  0  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  0  2  0  2  0  0  2  2  2  2  0  0  2  0  0  2  2  2
 0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  0  0  0  0  2  0  2  2  2  0  0  2  2  0  2  2  2  2  2  2  0  0  0  0  2  0  0  0  0  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+30x^89+23x^90+416x^91+24x^92+8x^94+7x^96+2x^121+1x^122

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 2.59 seconds.