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

generates a code of length 73 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+323x^68+48x^69+522x^70+176x^71+793x^72+576x^73+740x^74+176x^75+324x^76+48x^77+194x^78+126x^80+48x^82+1x^124

The gray image is a code over GF(2) with n=584, k=12 and d=272.
This code was found by Heurico 1.16 in 4.78 seconds.