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  0  X  2  X  0  X  2  X  0  X  2  X  X  X  0  X  2  X  X  X  X  1  1  1  1  1  1  X  X  X  X  1  1 2X 2X+2 2X 2X+2  X  X  X  X 2X 2X+2 2X 2X+2  1  1  1  1  X  X  X  X  X  X  X  1  X
 0  X  2 3X+2  0 3X+2  2 3X  0 3X+2  2 3X  0 3X+2  2  X 2X X+2 2X+2  X 2X X+2 2X+2 3X 2X X+2 2X+2  X 2X X+2 2X+2 3X 3X+2  X 3X  X 3X+2  X 3X  X 3X+2  X 3X  X  0  2 3X+2  X 3X  X  0  2  0  2  0 2X  2  2  2  2 X+2  X X+2  X  0 2X  X  X  X  X X+2  X X+2  X  X  X  X  X  0 2X  0 2X 2X+2 2X+2  2 2X 2X+2  0 2X 2X+2  2
 0  0 2X  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X  0 2X 2X  0  0  0  0 2X 2X  0
 0  0  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0  0 2X  0 2X 2X  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+60x^89+23x^90+352x^91+24x^92+32x^93+8x^94+7x^96+4x^105+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 0.875 seconds.