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

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+64x^60+72x^61+167x^62+280x^63+427x^64+586x^65+781x^66+970x^67+1158x^68+1380x^69+1529x^70+1612x^71+1547x^72+1428x^73+1154x^74+976x^75+724x^76+556x^77+378x^78+220x^79+134x^80+62x^81+66x^82+38x^83+26x^84+8x^85+13x^86+11x^88+4x^89+6x^90+4x^92+1x^94+1x^98

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 17.8 seconds.