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

generates a code of length 73 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+100x^67+185x^68+270x^69+350x^70+408x^71+498x^72+536x^73+494x^74+396x^75+338x^76+230x^77+162x^78+74x^79+9x^80+20x^81+2x^82+8x^83+4x^84+2x^87+3x^88+4x^91+1x^92+1x^112

The gray image is a code over GF(2) with n=584, k=12 and d=268.
This code was found by Heurico 1.16 in 0.985 seconds.