The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+82x^66+678x^67+1224x^68+1690x^69+2069x^70+1712x^71+2003x^72+2010x^73+1669x^74+1168x^75+854x^76+574x^77+305x^78+160x^79+72x^80+62x^81+34x^82+10x^83+4x^84+2x^88+1x^90

The gray image is a code over GF(2) with n=576, k=14 and d=264.
This code was found by Heurico 1.16 in 3.3 seconds.