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

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+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 7.39 seconds.