The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+224x^65+1468x^66+2722x^67+4139x^68+5480x^69+6833x^70+7692x^71+8546x^72+8294x^73+6620x^74+5390x^75+3865x^76+2176x^77+1133x^78+448x^79+327x^80+64x^81+70x^82+20x^83+14x^84+4x^86+4x^88+2x^89

The gray image is a code over GF(2) with n=576, k=16 and d=260.
This code was found by Heurico 1.16 in 39.5 seconds.