The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+152x^67+223x^68+478x^69+447x^70+542x^71+477x^72+566x^73+415x^74+420x^75+204x^76+98x^77+17x^78+34x^79+5x^80+2x^81+1x^82+4x^83+4x^85+4x^89+1x^100+1x^104

The gray image is a code over GF(2) with n=576, k=12 and d=268.
This code was found by Heurico 1.16 in 0.594 seconds.