The generator matrix

 1  0  1  1  1 X+2  1 2X+2  1  1  1 3X  1  1 2X  1 3X+2  1  1  2  1  X  1  1  1  1  1 2X+2  1  1 X+2  1  1 3X+2  1  0  1  X  1  1  1  1 2X  X  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  1  1  X  1  1  1  X  1  1  1  1  1  1  1  1  X  1  0  1 3X+2 2X  1 2X+2  1
 0  1 X+1 3X+2 2X+3  1  X  1 X+3 2X  1  1  2 X+1  1  3  1 2X+2 3X+3  1 2X+1  1  0 2X+2 X+2 3X X+1  1 3X  3  1 X+2 3X+1  1 2X+1  1 X+2  1 2X  1 3X+3 2X+2  1  1 2X+3 3X 2X+2 X+3  1  0 3X+2 X+2  0  0 3X  2 3X 2X+2  X 3X  0 2X+2  0  1 X+2 X+1  3 2X+2 X+2  1 3X+2 X+2  0 2X+2 3X 2X X+3 3X+3 3X+2  3  3 2X+3  1 2X  1 3X+2  1  1 2X+1  1  0
 0  0  2  2 2X+2  0 2X+2  0  2  2 2X+2  0 2X+2 2X  2 2X  2  0 2X  2 2X  2  0  0  0 2X 2X  0  0 2X  0  0  2  2 2X  0 2X+2 2X+2 2X+2  2 2X  0  2  0 2X+2  2  2 2X+2 2X+2 2X+2  2  2  2  0 2X  2  0 2X+2 2X+2 2X+2  0 2X 2X  2 2X  2 2X+2  0 2X  2  2 2X+2 2X+2 2X  0 2X+2  2 2X+2 2X  0 2X  0 2X+2 2X 2X 2X+2 2X  0  0 2X 2X
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0  0 2X  0 2X  0  0  0 2X  0 2X 2X 2X  0 2X  0  0 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X  0  0  0 2X 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X 2X
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X 2X 2X  0 2X  0 2X  0  0  0 2X 2X  0 2X  0 2X 2X 2X  0 2X  0 2X 2X  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0  0 2X 2X 2X  0 2X 2X  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+182x^86+356x^87+483x^88+338x^89+458x^90+594x^91+408x^92+300x^93+465x^94+264x^95+126x^96+62x^97+43x^98+2x^99+5x^100+2x^101+1x^102+2x^109+2x^110+1x^130+1x^132

The gray image is a code over GF(2) with n=728, k=12 and d=344.
This code was found by Heurico 1.16 in 1.17 seconds.