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

generates a code of length 74 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+114x^74+3x^76+4x^78+3x^80+2x^82+1x^92

The gray image is a code over GF(2) with n=592, k=7 and d=296.
This code was found by Heurico 1.16 in 0.25 seconds.