The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+56x^58+221x^60+56x^61+427x^62+200x^63+769x^64+344x^65+1072x^66+424x^67+1129x^68+424x^69+1064x^70+344x^71+735x^72+200x^73+385x^74+56x^75+181x^76+44x^78+20x^80+14x^82+11x^84+8x^86+3x^88+1x^90+2x^92+1x^94

The gray image is a linear code over GF(2) with n=272, k=13 and d=116.
This code was found by Heurico 1.16 in 4.47 seconds.