The generator matrix

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

generates a code of length 72 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+98x^66+612x^67+1160x^68+1922x^69+1685x^70+2072x^71+1907x^72+1980x^73+1544x^74+1462x^75+808x^76+558x^77+266x^78+160x^79+56x^80+52x^81+20x^82+14x^83+2x^84+2x^86+2x^88+1x^94

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 3.11 seconds.