The generator matrix

 1  0  0  1  1  1 2X  1  1  1 X+2 3X+2  1  X  1  1 2X  1  2 3X+2  1 3X  1  1 2X+2  X  0  1  1  1  1  1  1  1  1 X+2 3X  1  1  2  1  1 2X+2 3X+2  1 2X  1  1 3X 2X+2  X  1 2X  1  1 X+2 X+2  1  1  1  1  1  1  1  1  1 X+2  1  2  1  1  1  1
 0  1  0  0  3 2X+3  1 3X+2 X+1 2X  1  1 3X+1 2X+2 2X+2  1 X+2 2X+3  1  1 X+2  1  X 3X+2  1 X+2  1  X X+3  3  1 3X X+3 3X+1 2X+3  1  1 X+1  2 X+2  2 2X+2  1  1 2X  1 2X+1 3X 2X  2  1 3X  1 3X+2  2  1  1 2X+3 3X+3 X+2  0 X+2 3X+3  0  2  0  0  X  1 X+2 2X  2 2X
 0  0  1 X+1 3X+1  2 3X+3 2X+2 2X 2X+3 3X+3 2X  3  1 X+2  1  1  X 2X+1 X+2 X+1 2X+3  3 3X+2 2X  1 X+2 X+3  2  1 2X+2  0 3X 2X+1 3X+1 X+3  X X+1 2X  1 3X+1 X+2 3X+1 2X+2  1 2X+1 3X+3  1  1  1  0 2X+2  X X+2 2X+3  3 3X X+2 X+3 X+3  2  0  3 X+3 3X+3 2X+3  1 2X+3 X+3 2X+1 3X X+1 2X
 0  0  0 2X 2X 2X  0 2X  0  0 2X 2X  0 2X  0 2X 2X 2X 2X  0 2X  0 2X 2X 2X 2X  0  0 2X  0  0  0  0 2X  0  0 2X  0 2X  0  0 2X 2X  0 2X  0 2X  0  0  0 2X 2X 2X  0 2X 2X  0  0 2X  0  0 2X  0 2X  0 2X  0  0  0 2X  0 2X  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+106x^68+540x^69+1001x^70+1308x^71+1051x^72+1114x^73+890x^74+650x^75+467x^76+402x^77+228x^78+166x^79+129x^80+104x^81+22x^82+4x^83+4x^84+3x^86+1x^92+1x^96

The gray image is a code over GF(2) with n=584, k=13 and d=272.
This code was found by Heurico 1.16 in 0.984 seconds.