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

generates a code of length 93 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+128x^89+63x^90+260x^91+193x^92+808x^93+190x^94+192x^95+61x^96+120x^97+3x^98+28x^99+1x^180

The gray image is a code over GF(2) with n=744, k=11 and d=356.
This code was found by Heurico 1.16 in 1.05 seconds.