The generator matrix

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

generates a code of length 75 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+142x^68+544x^69+1539x^70+2110x^71+2885x^72+3484x^73+4116x^74+4222x^75+3756x^76+3002x^77+2569x^78+1874x^79+1285x^80+560x^81+373x^82+144x^83+71x^84+38x^85+12x^86+16x^87+11x^88+4x^89+7x^90+2x^91+1x^92

The gray image is a code over GF(2) with n=600, k=15 and d=272.
This code was found by Heurico 1.16 in 12.7 seconds.