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  X  1  1  X  1  X  1  1  1  1  1  1  2  1  1  0  1 2X  1  2  1  1 2X  1
 0  X  0  X 2X  0 3X  X  2 X+2  2 X+2 2X+2 3X+2  2 X+2  0 2X 3X 3X  0  2 3X X+2  2 3X+2 2X X+2 2X+2 X+2 2X+2  X  0  2  X  X 2X+2 3X 2X 3X  2 3X 2X+2 2X+2 X+2 3X+2  0 3X+2 2X 2X+2 X+2  2 2X+2 3X 3X  0 X+2 3X  0 X+2  X 3X+2 3X+2  X 2X+2 2X+2 3X+2  X X+2 2X+2  X X+2
 0  0  X  X  2 X+2 X+2  2  2 3X+2  X 2X+2  0 3X X+2 2X  0 3X+2 X+2 2X+2 2X+2 X+2 3X 2X+2 2X+2 3X+2 3X 2X 2X 3X 3X  0 2X 3X 3X 2X X+2  2 2X+2 3X+2  X 2X 2X+2 2X+2 3X+2 X+2 3X 2X  X  0  X 3X+2 3X+2  0  X 2X+2  X 3X 3X+2  0 X+2  0  X 2X  2  X 2X+2 3X 3X 3X+2  0  0
 0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0 2X 2X  0 2X  0 2X 2X 2X 2X  0 2X 2X  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+119x^68+210x^69+211x^70+358x^71+366x^72+358x^73+136x^74+104x^75+69x^76+46x^77+49x^78+10x^79+4x^80+2x^81+4x^82+1x^128

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 0.421 seconds.