The generator matrix

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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+54x^57+112x^58+216x^59+314x^60+336x^61+461x^62+540x^63+690x^64+982x^65+1121x^66+1270x^67+1430x^68+1358x^69+1390x^70+1304x^71+1126x^72+994x^73+749x^74+596x^75+403x^76+300x^77+204x^78+156x^79+111x^80+66x^81+48x^82+14x^83+12x^84+6x^85+8x^86+8x^88+1x^90+1x^92+1x^98+1x^110

The gray image is a linear code over GF(2) with n=276, k=14 and d=114.
This code was found by Heurico 1.16 in 22.5 seconds.