The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+156x^86+824x^87+960x^88+1318x^89+848x^90+1016x^91+634x^92+800x^93+365x^94+496x^95+211x^96+234x^97+108x^98+88x^99+96x^100+24x^101+4x^102+2x^104+5x^106+1x^114+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 1.55 seconds.