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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+74x^59+132x^60+174x^61+292x^62+392x^63+515x^64+598x^65+735x^66+918x^67+1091x^68+1290x^69+1393x^70+1350x^71+1328x^72+1244x^73+1091x^74+958x^75+746x^76+578x^77+410x^78+316x^79+229x^80+190x^81+153x^82+82x^83+43x^84+22x^85+14x^86+6x^87+6x^88+5x^90+4x^92+2x^94+1x^96+1x^102

The gray image is a linear code over GF(2) with n=284, k=14 and d=118.
This code was found by Heurico 1.16 in 30.7 seconds.