The generator matrix

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

generates a code of length 75 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+198x^67+1267x^68+2948x^69+5205x^70+7462x^71+11206x^72+12828x^73+16362x^74+16224x^75+16595x^76+13712x^77+10704x^78+6760x^79+4960x^80+2416x^81+1294x^82+554x^83+176x^84+92x^85+64x^86+34x^87+2x^88+4x^89+2x^90+1x^94+1x^96

The gray image is a code over GF(2) with n=600, k=17 and d=268.
This code was found by Heurico 1.16 in 161 seconds.