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

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+43x^66+104x^68+238x^70+1233x^72+256x^73+52x^74+40x^76+34x^78+21x^80+17x^82+8x^84+1x^136

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 7.27 seconds.