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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+240x^60+524x^62+32x^63+793x^64+180x^65+1154x^66+436x^67+1601x^68+908x^69+1848x^70+1044x^71+1941x^72+788x^73+1592x^74+508x^75+1158x^76+164x^77+630x^78+28x^79+436x^80+8x^81+220x^82+87x^84+46x^86+12x^88+2x^90+2x^92+1x^104

The gray image is a linear code over GF(2) with n=284, k=14 and d=120.
This code was found by Heurico 1.16 in 27.3 seconds.