The generator matrix

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

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+98x^60+44x^61+285x^62+272x^63+467x^64+472x^65+632x^66+792x^67+656x^68+960x^69+608x^70+744x^71+566x^72+520x^73+393x^74+232x^75+185x^76+52x^77+103x^78+8x^79+55x^80+20x^82+12x^84+4x^86+6x^88+3x^90+1x^92+1x^96

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 4.64 seconds.