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

generates a code of length 75 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+124x^71+144x^72+288x^73+336x^74+384x^75+312x^76+240x^77+47x^78+60x^79+35x^80+48x^81+16x^82+8x^83+4x^84+1x^142

The gray image is a code over GF(2) with n=600, k=11 and d=284.
This code was found by Heurico 1.16 in 0.562 seconds.