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

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+212x^60+612x^61+1012x^62+1456x^63+1838x^64+2176x^65+2149x^66+2788x^67+2720x^68+2980x^69+2665x^70+2834x^71+2515x^72+2014x^73+1588x^74+1316x^75+778x^76+530x^77+281x^78+130x^79+92x^80+50x^81+17x^82+4x^83+4x^84+6x^85

The gray image is a linear code over GF(2) with n=276, k=15 and d=120.
This code was found by Heurico 1.16 in 43.6 seconds.