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

generates a code of length 75 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+26x^72+160x^73+226x^74+208x^75+228x^76+136x^77+28x^78+1x^80+8x^81+1x^82+1x^130

The gray image is a code over GF(2) with n=600, k=10 and d=288.
This code was found by Heurico 1.16 in 0.594 seconds.