The generator matrix

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

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+48x^66+123x^68+96x^69+137x^70+416x^71+447x^72+416x^73+119x^74+96x^75+82x^76+39x^78+11x^80+9x^82+6x^84+1x^88+1x^132

The gray image is a code over GF(2) with n=576, k=11 and d=264.
This code was found by Heurico 1.16 in 0.484 seconds.