The generator matrix

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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+62x^87+298x^88+306x^89+383x^90+222x^91+280x^92+130x^93+153x^94+72x^95+52x^96+36x^97+38x^98+4x^99+4x^100+1x^102+4x^104+1x^120+1x^130

The gray image is a code over GF(2) with n=728, k=11 and d=348.
This code was found by Heurico 1.16 in 0.609 seconds.