The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+95x^58+20x^59+423x^60+60x^61+525x^62+132x^63+795x^64+352x^65+826x^66+452x^67+993x^68+464x^69+789x^70+348x^71+731x^72+144x^73+433x^74+72x^75+252x^76+4x^77+125x^78+112x^80+22x^82+19x^84+1x^86+1x^88+1x^92

The gray image is a code over GF(2) with n=272, k=13 and d=116.
This code was found by Heurico 1.16 in 6.13 seconds.