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

generates a code of length 93 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+4x^92+94x^93+6x^94+12x^95+2x^96+6x^97+1x^100+1x^106+1x^110

The gray image is a code over GF(2) with n=744, k=7 and d=368.
This code was found by Heurico 1.16 in 0.593 seconds.