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

generates a code of length 74 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+226x^72+576x^74+216x^76+4x^80+1x^144

The gray image is a code over GF(2) with n=592, k=10 and d=288.
This code was found by Heurico 1.16 in 0.594 seconds.