The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+196x^67+1250x^68+2942x^69+5241x^70+7872x^71+10173x^72+14116x^73+15051x^74+17450x^75+15686x^76+13786x^77+10713x^78+7280x^79+4510x^80+2768x^81+1152x^82+540x^83+172x^84+96x^85+32x^86+18x^87+14x^88+2x^89+3x^90+2x^91+2x^92+2x^95+2x^97

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 164 seconds.