The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+40x^57+81x^58+158x^59+243x^60+420x^61+569x^62+760x^63+951x^64+1148x^65+1409x^66+1560x^67+1712x^68+1568x^69+1471x^70+1212x^71+927x^72+772x^73+479x^74+346x^75+225x^76+136x^77+67x^78+44x^79+18x^80+8x^81+15x^82+16x^83+10x^84+4x^85+5x^86+7x^88+2x^92

The gray image is a linear code over GF(2) with n=272, k=14 and d=114.
This code was found by Heurico 1.16 in 29.1 seconds.