The generator matrix

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

generates a code of length 75 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+99x^70+280x^71+615x^72+416x^73+641x^74+352x^75+464x^76+360x^77+391x^78+184x^79+151x^80+48x^81+37x^82+16x^83+9x^84+8x^85+14x^86+4x^88+2x^90+2x^92+1x^100+1x^104

The gray image is a code over GF(2) with n=600, k=12 and d=280.
This code was found by Heurico 1.16 in 0.657 seconds.