The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+73x^68+336x^69+281x^70+284x^71+239x^72+232x^73+197x^74+240x^75+70x^76+54x^77+30x^78+4x^79+2x^82+1x^86+1x^90+1x^92+2x^93

The gray image is a code over GF(2) with n=576, k=11 and d=272.
This code was found by Heurico 1.16 in 0.406 seconds.