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

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

Homogenous weight enumerator: w(x)=1x^0+132x^89+82x^90+128x^91+502x^92+392x^93+489x^94+116x^95+63x^96+112x^97+12x^98+12x^99+2x^100+4x^101+1x^182

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 23.8 seconds.