The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+71x^66+722x^67+1118x^68+1580x^69+1814x^70+2296x^71+2008x^72+2052x^73+1523x^74+1224x^75+787x^76+550x^77+285x^78+194x^79+40x^80+72x^81+18x^82+10x^83+11x^84+2x^85+1x^86+2x^87+3x^88

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 3.53 seconds.