The generator matrix

 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  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  X  1  1 2X  X  1
 0  X  0 3X+2 2X X+2 2X 3X  0 X+2 2X 3X 2X 3X+2  0  X 2X 3X+2  0 3X  0 X+2  0  X 3X+2  0 3X+2 2X  0 3X 2X  X  2 3X+2 2X+2 3X  2 3X+2  2 3X  2 X+2  2 3X 2X+2 3X  2 3X+2  2 3X+2 X+2 2X+2  2 3X  2 3X  X  2 3X+2 2X+2  2  X X+2  2 X+2 3X+2  0 2X+2 2X+2 2X+2 2X+2 X+2  X  0 2X 3X+2 X+2 3X+2 3X 2X+2 2X+2  2 2X+2 2X  X 3X+2  0 2X+2  X X+2  0
 0  0 2X+2  0  0 2X+2  2  2  0  0  0  0  2 2X+2 2X+2  2 2X 2X 2X 2X 2X+2  2  2 2X+2 2X 2X+2  2 2X 2X 2X  2 2X+2  2  2 2X+2 2X+2  0 2X 2X  0  2  2  2  2  0  0  0  0 2X+2 2X+2  0 2X 2X 2X  2 2X+2  2 2X+2 2X 2X+2  0 2X 2X+2 2X 2X+2  2  2 2X+2  2  0 2X  0  0  0 2X+2  0 2X+2 2X+2 2X 2X  0 2X+2  2 2X 2X+2 2X  0  2 2X 2X+2 2X
 0  0  0 2X+2  2 2X+2  2  0 2X  2 2X+2 2X 2X+2  2 2X 2X  0  2  2  0 2X+2  2 2X 2X 2X+2  2 2X+2 2X+2 2X 2X  0  0  0  0 2X+2  2 2X+2  0 2X 2X+2 2X 2X  2 2X+2  2  2 2X  0 2X 2X 2X  0 2X+2 2X+2 2X+2 2X+2  2  2 2X  0  0  2  0  2  2 2X  2 2X 2X 2X 2X  0  2  2  2 2X 2X 2X+2  2  2 2X+2 2X+2  0 2X 2X 2X+2 2X+2  2 2X+2  2  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+174x^87+77x^88+120x^89+380x^90+572x^91+362x^92+116x^93+64x^94+162x^95+8x^96+4x^97+2x^98+4x^99+1x^102+1x^174

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 62.5 seconds.