The generator matrix

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

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+98x^67+712x^68+1140x^69+1623x^70+1960x^71+2028x^72+2188x^73+1790x^74+1618x^75+1157x^76+802x^77+579x^78+284x^79+216x^80+60x^81+52x^82+38x^83+28x^84+2x^85+4x^86+1x^88+2x^91+1x^92

The gray image is a code over GF(2) with n=584, k=14 and d=268.
This code was found by Heurico 1.16 in 3.16 seconds.