The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+136x^67+790x^68+672x^69+1354x^70+884x^71+1282x^72+704x^73+916x^74+364x^75+419x^76+232x^77+234x^78+52x^79+112x^80+24x^81+8x^82+4x^83+3x^84+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 0.922 seconds.