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

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

Homogenous weight enumerator: w(x)=1x^0+27x^86+120x^87+70x^88+206x^89+233x^90+762x^91+212x^92+204x^93+65x^94+108x^95+21x^96+6x^97+10x^98+2x^99+1x^178

The gray image is a code over GF(2) with n=728, k=11 and d=344.
This code was found by Heurico 1.16 in 1.31 seconds.