The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1 X+2  1  1 2X+2  1 3X  1  1  1  1  1  1  1  1  1  0 X+2 2X+2 3X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X+2  3  1 3X+3 2X+2  1 3X 2X+1  1  0 X+1  1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+1  1 X+2  3  1 2X+2 3X+3  1 3X  1 2X+1 2X+3 X+1  1 3X+3  0 X+2 2X+2 3X  1  1  1  1  3 3X+1 X+3 2X+1  3 X+1 2X+1 3X+3 X+1  3 2X+3 3X+1 3X+3 X+3 2X+1  1 2X  2 3X+2  X  0 2X+2 X+2 3X+2
 0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X  0  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X 2X 2X 2X  0 2X  0  0  0
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X  0  0 2X 2X 2X  0 2X  0  0  0 2X 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0  0  0 2X 2X 2X  0 2X 2X 2X  0 2X  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0  0 2X  0  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0  0 2X 2X 2X  0  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 68.

Homogenous weight enumerator: w(x)=1x^0+244x^68+64x^69+240x^70+64x^71+820x^72+64x^73+240x^74+64x^75+244x^76+1x^80+1x^96+1x^112

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 0.282 seconds.