The generator matrix

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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+332x^62+552x^63+1152x^64+1452x^65+1862x^66+1900x^67+2410x^68+2276x^69+2958x^70+2904x^71+2992x^72+2544x^73+2546x^74+1924x^75+1764x^76+1172x^77+898x^78+488x^79+353x^80+108x^81+92x^82+40x^83+26x^84+12x^86+6x^88+4x^90

The gray image is a linear code over GF(2) with n=284, k=15 and d=124.
This code was found by Heurico 1.13 in 15 seconds.