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  1  X  1  1  1  X  X
 0  X  0  X 2X 2X 3X 3X  2 X+2  2 X+2 2X+2 3X+2 2X+2 3X+2  0 3X  0 X+2 X+2  X  0  2 2X+2 X+2  0 3X 2X+2 X+2  2  X  0 2X+2 3X 3X 2X+2 3X+2 X+2 2X 2X+2 3X  0  X 2X 2X+2 3X+2 X+2  2 3X+2 3X 2X 3X 2X 2X+2 X+2 3X  0  0 2X+2 X+2  X 3X+2  2  0  2 3X X+2  X 3X+2  0 2X  2 3X+2 2X X+2  0 3X+2  X 2X 2X+2 2X+2 3X+2 3X+2  X X+2  2 X+2 2X+2  X 3X+2
 0  0  X  X  2 3X+2 X+2 2X+2  2 X+2  X  0  0  X 3X+2 2X+2  0 X+2  X 2X+2 3X+2  2  2 3X 2X+2 2X X+2  X 2X 3X 3X+2  0 2X 3X  X  2  2 X+2  0 X+2 X+2 2X  2 X+2 3X  0  2  X 2X  0  2 3X+2 3X+2 2X X+2  X 3X 3X 2X+2  2 3X+2 2X  2 3X 2X+2  X  0 2X+2  X 3X 3X+2  2 2X+2 X+2  X 3X 3X 2X+2 X+2 X+2  X 2X+2 2X 2X 3X+2  0  0  2  0  2 2X+2
 0  0  0 2X 2X 2X  0 2X  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X  0 2X 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0  0  0 2X 2X  0  0  0 2X 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0 2X  0  0  0  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+168x^87+68x^88+196x^89+200x^90+820x^91+176x^92+188x^93+52x^94+148x^95+10x^96+16x^97+4x^98+1x^176

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 1 seconds.