The generator matrix

 1  0  0  0  1  1  1  1 X^2  1 X^2+X  X  1 X^2  1  1  1  X  1  1  X  0  1  X  0  1  1  0 X^2+X  1 X^2+X  1  1  X  1 X^2+X  1 X^2  1  1 X^2+X X^2 X^2  0  1  1 X^2  X  X  1  1  1 X^2 X^2  1 X^2+X  1  1  1  X  1  1  1  0  1  1  1  1  1
 0  1  0  0  0 X^2  1 X^2+1  1 X^2+X+1 X^2  1  0  1 X^2+1 X^2  1  1  X X+1  1  1 X^2 X^2+X X^2+X X^2+X+1  1 X^2+X  1 X^2+X  X X^2+1  0  1  0  1 X^2+X  1  X X^2+X+1 X^2+X X^2+X  1  1 X^2+1  X  1  1  1 X+1 X^2 X+1  0  1  1  1 X^2+X+1 X^2+X+1  X  1  X  0  0  1 X^2+1  1 X^2+X+1 X^2+X+1  0
 0  0  1  0  0 X^2+1  1 X^2+X X+1 X^2+1  1 X^2 X^2+X+1 X^2+1  X  X X^2+X+1 X^2+X+1 X^2 X^2 X+1 X^2+X X^2+1  1  1 X^2+X X^2+X+1 X^2+X  0 X+1  1 X^2+X+1 X^2+X X^2+1  0  X  0 X+1 X+1 X^2  1  0 X^2+1  0 X^2+X X^2+X+1 X^2  0  0 X^2 X+1 X^2+X  1  X X^2+X X^2+X X^2+X  1 X^2+X X^2+1  1 X+1  1 X^2+1 X^2+X X^2+X+1 X^2+X+1  0  0
 0  0  0  1  1  1 X^2 X+1 X+1 X^2+1 X^2+1 X^2+1  X  X  0 X^2+1 X+1 X+1 X^2  X  0 X^2+X+1 X+1  X  1 X^2+X+1 X^2+1  1 X^2+X  0 X^2 X^2 X^2+X X^2+X  1  0 X^2+X X^2+X+1 X^2+1  0 X+1  1 X^2+X+1 X^2+1 X^2+1 X^2+X  1 X^2 X^2+X+1 X^2  0  1  X X^2+X+1  X X^2+1 X^2+X X^2+X+1  1 X^2+X X+1  0  1  1 X^2+X+1 X+1 X^2+1 X^2  0
 0  0  0  0  X  0  0  0  0  X  X  X X^2+X  X  X X^2+X  X X^2 X^2+X  0  0 X^2 X^2+X X^2+X X^2  X  0 X^2+X X^2+X  0 X^2+X X^2+X  0 X^2 X^2 X^2+X  0  X  X X^2 X^2  0 X^2  X  0 X^2  0 X^2  X  X  0 X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X  0  0  X  X X^2+X X^2 X^2+X  0  X  X  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+65x^60+338x^61+486x^62+778x^63+734x^64+1216x^65+1130x^66+1566x^67+1311x^68+1612x^69+1166x^70+1444x^71+967x^72+1156x^73+722x^74+702x^75+378x^76+248x^77+130x^78+118x^79+58x^80+32x^81+8x^82+6x^84+6x^85+6x^86

The gray image is a linear code over GF(2) with n=276, k=14 and d=120.
This code was found by Heurico 1.13 in 4.03 seconds.