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  1  X  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  X  1  2  2  X
 0 2X+2  0  0  0  2 2X+2  2  0 2X 2X+2 2X+2  0 2X 2X+2 2X+2  0 2X 2X 2X 2X+2 2X+2  2 2X+2  2  0  2  0 2X  0 2X+2 2X+2  2  0  2  0 2X+2 2X 2X  0 2X+2  2  0 2X+2  2 2X+2 2X  0  2  2  0  2 2X+2 2X 2X+2  2 2X 2X  0 2X  2 2X+2  0  2  2  0 2X 2X  2 2X 2X  2
 0  0 2X+2  0  2  2  2 2X  0 2X  2 2X+2  2  2 2X 2X  0 2X+2 2X+2  0  0  0 2X+2 2X+2 2X+2 2X 2X  0  2 2X+2  0 2X+2 2X+2 2X  0  2  2  0  0  2  2  0  2  2  0 2X  0  2 2X  0 2X  2 2X 2X  2 2X+2 2X+2 2X+2  2  2 2X 2X 2X  0 2X  2  2 2X+2 2X+2  2 2X+2  2
 0  0  0 2X+2  2 2X 2X+2 2X+2  0 2X+2 2X 2X+2  2  0 2X+2  0 2X 2X+2 2X  2 2X  2 2X 2X+2  2 2X+2 2X 2X  2 2X 2X+2  0  0 2X 2X+2 2X 2X  0 2X+2 2X+2  2 2X 2X+2  2 2X  2 2X+2 2X  2  2  0  0 2X 2X  0  0  0  0  0 2X+2 2X+2  2  2  2  0  0  0  2  2 2X 2X+2  0
 0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X 2X  0 2X 2X  0 2X  0 2X  0  0  0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0 2X  0  0  0  0  0 2X  0 2X 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+61x^66+98x^68+48x^69+272x^70+240x^71+715x^72+144x^73+253x^74+80x^75+47x^76+51x^78+32x^80+2x^82+2x^84+1x^86+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 0.469 seconds.