The generator matrix

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

generates a code of length 74 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+710x^68+1088x^69+2594x^70+2472x^71+4117x^72+3824x^73+4212x^74+3496x^75+3698x^76+2296x^77+2006x^78+944x^79+760x^80+184x^81+232x^82+32x^83+77x^84+12x^86+10x^88+3x^92

The gray image is a code over GF(2) with n=592, k=15 and d=272.
This code was found by Heurico 1.16 in 798 seconds.