The generator matrix

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

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+79x^68+304x^69+528x^70+500x^71+474x^72+524x^73+444x^74+452x^75+338x^76+190x^77+154x^78+54x^79+9x^80+20x^81+15x^82+2x^85+1x^86+2x^88+1x^90+1x^92+1x^94+2x^95

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 0.515 seconds.