The generator matrix

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

generates a code of length 91 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+180x^87+720x^88+672x^89+680x^90+404x^91+408x^92+184x^93+280x^94+100x^95+173x^96+128x^97+84x^98+36x^99+16x^100+24x^101+1x^102+2x^104+2x^106+1x^110

The gray image is a code over GF(2) with n=728, k=12 and d=348.
This code was found by Heurico 1.16 in 0.578 seconds.