The generator matrix

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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+173x^86+734x^87+1160x^88+1108x^89+1003x^90+922x^91+791x^92+620x^93+487x^94+378x^95+232x^96+196x^97+161x^98+78x^99+54x^100+60x^101+25x^102+1x^104+6x^106+1x^108+1x^110

The gray image is a code over GF(2) with n=728, k=13 and d=344.
This code was found by Heurico 1.16 in 1.36 seconds.