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

generates a code of length 72 over Z2[X]/(X^4) 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 linear code over GF(2) with n=576, k=11 and d=264.
This code was found by Heurico 1.16 in 0.484 seconds.