The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+316x^72+64x^73+168x^74+256x^75+208x^76+8x^78+1x^80+1x^96+1x^112

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 0.312 seconds.