The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+288x^87+42x^88+200x^89+224x^90+656x^91+198x^92+32x^93+32x^94+336x^95+12x^96+24x^97+2x^116+1x^128

The gray image is a code over GF(2) with n=728, k=11 and d=348.
This code was found by Heurico 1.16 in 0.625 seconds.