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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+212x^58+546x^60+52x^61+773x^62+176x^63+1170x^64+456x^65+1489x^66+808x^67+1897x^68+1008x^69+2089x^70+936x^71+1657x^72+504x^73+1041x^74+120x^75+622x^76+28x^77+411x^78+8x^79+225x^80+119x^82+22x^84+7x^86+3x^88+3x^90+1x^100

The gray image is a linear code over GF(2) with n=276, k=14 and d=116.
This code was found by Heurico 1.16 in 23.8 seconds.