The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+222x^59+574x^60+1192x^61+1189x^62+1918x^63+1857x^64+2680x^65+2288x^66+3116x^67+2485x^68+3408x^69+2481x^70+2764x^71+1811x^72+1866x^73+1035x^74+826x^75+463x^76+310x^77+98x^78+110x^79+39x^80+14x^81+9x^82+4x^83+2x^84+2x^85+4x^86

The gray image is a linear code over GF(2) with n=272, k=15 and d=118.
This code was found by Heurico 1.16 in 41.3 seconds.