The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  X  1  1 X^2+2  1  1  2  1  1 X^2+X  1  1 X^2  1  1 X+2  1  1  0  1  1 X^2+X+2  1  1  X  1  1 X^2+2  1  1  1  1 X+2  2  1  1  1  1 X^2 X^2+X  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  0  2 X^2+X X^2  X  0 X^2+2  X X^2+X+2  0  1
 0  1 X+1 X^2+X+2 X^2+1  1  X X^2+X+1  1 X^2+2  3  1  2 X+1  1 X^2+X X^2+3  1 X+2 X^2+X+3  1 X^2  1  1  0 X+1  1 X^2+X+2  1  1 X^2+2 X^2+X+3  1  X X^2+3  1  2 X^2+X X+1 X^2+1  1  1 X^2 X+2 X^2+X+1  3  1  1  2 X^2+X X^2 X+2  0 X^2+X+2 X^2+2  X  2 X^2+X X^2 X+2  0 X^2+X+2 X^2+2  X X+3 X^2+1 X^2+X+1  3 X+3 X^2+3 X^2+X+3  1 X+3 X^2+1 X^2+X+1  3 X+3 X^2+3 X^2+X+3  1  0  1  1  1  1  1  1 X^2+X+2  1  1  0
 0  0 X^2 X^2+2  2 X^2 X^2 X^2+2 X^2+2  2  0  2 X^2  0 X^2  0 X^2  0  2  2 X^2+2 X^2+2 X^2+2  2  2  2  2 X^2 X^2 X^2+2  0  0 X^2 X^2+2 X^2+2  0 X^2+2  2 X^2+2  0  0 X^2+2 X^2  0 X^2  2 X^2  2  2 X^2+2  0 X^2 X^2+2  2 X^2  0  0 X^2  2 X^2+2 X^2  0 X^2+2  2  2 X^2+2  0 X^2 X^2  2 X^2+2  0  0 X^2  2 X^2+2 X^2+2  0 X^2  2 X^2  2 X^2+2  0  2 X^2+2 X^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 89.

Homogenous weight enumerator: w(x)=1x^0+116x^89+236x^90+360x^91+190x^92+84x^93+18x^94+16x^95+1x^112+1x^114+1x^130

The gray image is a code over GF(2) with n=728, k=10 and d=356.
This code was found by Heurico 1.16 in 0.672 seconds.