The generator matrix

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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+38x^60+116x^61+249x^62+322x^63+487x^64+552x^65+568x^66+708x^67+725x^68+764x^69+803x^70+728x^71+533x^72+496x^73+377x^74+238x^75+202x^76+104x^77+52x^78+36x^79+14x^80+16x^81+21x^82+14x^83+15x^84+8x^86+2x^87+1x^88+2x^90

The gray image is a linear code over GF(2) with n=276, k=13 and d=120.
This code was found by Heurico 1.16 in 4.84 seconds.