The generator matrix

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

generates a code of length 74 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+82x^67+565x^68+1272x^69+2336x^70+2558x^71+4231x^72+3610x^73+4366x^74+3454x^75+3768x^76+2406x^77+1870x^78+1050x^79+638x^80+186x^81+190x^82+80x^83+49x^84+10x^85+30x^86+8x^87+4x^88+4x^89

The gray image is a code over GF(2) with n=592, k=15 and d=268.
This code was found by Heurico 1.16 in 12.3 seconds.