The generator matrix

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

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+489x^68+360x^69+540x^70+448x^71+569x^72+368x^73+536x^74+320x^75+370x^76+40x^77+12x^78+23x^80+11x^84+5x^88+2x^92+2x^96

The gray image is a code over GF(2) with n=576, k=12 and d=272.
This code was found by Heurico 1.16 in 26.9 seconds.