The generator matrix

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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+64x^59+324x^60+640x^61+863x^62+1296x^63+1658x^64+2214x^65+2177x^66+2930x^67+2607x^68+3234x^69+2801x^70+2892x^71+2200x^72+2206x^73+1588x^74+1220x^75+752x^76+490x^77+284x^78+156x^79+61x^80+44x^81+27x^82+18x^83+13x^84+4x^85+3x^86+1x^94

The gray image is a linear code over GF(2) with n=276, k=15 and d=118.
This code was found by Heurico 1.16 in 44.2 seconds.