The generator matrix

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

generates a code of length 73 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+148x^69+692x^70+562x^71+752x^72+432x^73+444x^74+300x^75+241x^76+128x^77+205x^78+82x^79+93x^80+8x^81+1x^84+4x^85+1x^86+2x^90

The gray image is a code over GF(2) with n=584, k=12 and d=276.
This code was found by Heurico 1.16 in 0.312 seconds.