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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+154x^90+56x^92+36x^94+3x^96+4x^100+2x^106

The gray image is a code over GF(2) with n=728, k=8 and d=360.
This code was found by Heurico 1.16 in 0.719 seconds.