The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+386x^69+358x^70+216x^71+223x^72+224x^73+264x^74+276x^75+46x^76+30x^77+4x^79+1x^80+16x^81+1x^90+1x^96+1x^98

The gray image is a code over GF(2) with n=576, k=11 and d=276.
This code was found by Heurico 1.16 in 61.1 seconds.