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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+74x^85+229x^86+274x^87+370x^88+468x^89+401x^90+624x^91+392x^92+416x^93+287x^94+210x^95+174x^96+68x^97+33x^98+24x^99+18x^100+10x^101+9x^102+4x^103+4x^104+4x^105+1x^110+1x^152

The gray image is a code over GF(2) with n=728, k=12 and d=340.
This code was found by Heurico 1.16 in 1.28 seconds.