The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+208x^86+644x^87+1127x^88+1276x^89+927x^90+806x^91+892x^92+684x^93+433x^94+348x^95+247x^96+208x^97+218x^98+90x^99+18x^100+40x^101+16x^102+2x^104+5x^106+1x^112+1x^118

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 1.42 seconds.