The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+80x^67+778x^68+806x^69+1238x^70+930x^71+1254x^72+798x^73+816x^74+412x^75+440x^76+228x^77+243x^78+50x^79+70x^80+22x^81+22x^82+2x^85+1x^86+1x^88

The gray image is a code over GF(2) with n=576, k=13 and d=268.
This code was found by Heurico 1.16 in 0.954 seconds.