The generator matrix

 1  0  1  1  1 3X+2  X  1  1 2X  1  1  2  1  1  1 X+2  1  1 2X+2  1 3X  1  1  1  1  1 3X  1  0  1  1  1  1  1 2X 3X+2  1  1  1  1  2 3X  1 3X 2X  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  2  1  1
 0  1 X+1 X+2 2X+3  1  1 2X+2 X+3  1 3X  1  1 2X X+1 3X+2  1 3X+3  2  1  X  1 X+1 3X+3  3 2X+1  0  1  3  1 3X+2 3X+1  2 2X+3 X+2  1  1 2X+1 2X+2 3X X+2  1  1 3X+1  1  1 2X  1  0  X  2 3X 2X  2 2X+2 3X  X X+2  2 X+2  2 X+2  2 X+2 3X 2X 2X 3X+2  1 3X+1  X 3X 3X
 0  0  2  0 2X+2  2  2  0 2X+2 2X+2  0  2 2X+2  2 2X 2X+2  0 2X  2  0 2X+2  0 2X 2X  0 2X  0  0 2X  0 2X+2  2  2 2X+2 2X  2  2  0  0 2X  2  2 2X  2  2 2X 2X+2 2X+2 2X+2 2X+2 2X  2  2  0 2X  0  0 2X 2X 2X 2X+2 2X+2  0  0  2  2 2X 2X 2X 2X+2  2  0 2X
 0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X  0  0  0 2X  0 2X  0  0  0 2X 2X 2X 2X  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X  0  0  0
 0  0  0  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0 2X  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0 2X  0 2X 2X  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X  0 2X 2X  0 2X 2X  0  0  0  0  0  0 2X  0 2X 2X  0  0 2X 2X 2X  0 2X 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+160x^68+252x^69+426x^70+428x^71+562x^72+592x^73+418x^74+384x^75+486x^76+244x^77+80x^78+20x^79+23x^80+2x^82+12x^84+2x^86+2x^88+2x^108

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 0.609 seconds.