The generator matrix

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

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+144x^71+678x^72+648x^73+756x^74+368x^75+386x^76+288x^77+276x^78+200x^79+160x^80+72x^81+80x^82+8x^83+28x^84+3x^88

The gray image is a code over GF(2) with n=600, k=12 and d=284.
This code was found by Heurico 1.16 in 0.329 seconds.