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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  1  X  X  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  X  X  X  X  0  0  0  X  0  X  X  0  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  X  X  X  0  0  X  0  0  X  0  X  X  X  0  X  0  X  0  X  X  X  0  0  X  0  0  0  X  X  0  X  0  0  X  0  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  X  X  0  0  0  X  0  0  0  X  X  X  0  X  0  0  X  X  0  0  0  X  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  0  X  X  0  X  X  0  0  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  X  0  0  0  0  X  0  X  X  X  0  X  0  0  X  0  0  X  X  0  0  X  X  X  X  0  X  X  X  X  X  0  X  0  X  0  X  X  0  0  X  X  X  X  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  X  X  0  X  X  X  0  0  0  X  X  X  X  X  0  X  0  X  0  0  0  X  X  0  0  X  X  X  0  0  0  X  0  0  X  0  0  0  0  0  X  0  X  0  0  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  0  X  X  0  X  0  X  0  X  X  X  X  0  0  X  X  0  0  0  X  X  0  X  X  X  X  0  X  X  0  X  X  0  X  X  0  0  X  0  X  X  0  X  X  0  0  0  X  X  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  X  0  X  X  0  X  0  X  0  0  X  0  0  X  X  X  0  0  0  X  0  0  0  0  X  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  0  X  0  X  0  X  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  X  X  0  X  0  0  0  X  X  X  0  0  X  0  X  X  X  X  0  0  0  0  0  X  X  X  0  X  X  X  X  0  X  0  0  0  X  X  X  X  X  0  X  0  0  X  X  0  0  X  0  X  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  0  0  X  0  X  0  0  X  0  0  0  0  X  X  X  0  0  X  X  0  X  X  0  X  0  0  X  0  X  X  0  0  0  X  0  X  0  X  X  0  0  X  0  0  0  X  X  X  X  X  0  0  0  X
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  0  0  X  0  0  X  X  0  0  X  0  X  X  0  0  X  X  0  X  X  0  X  X  0  0  0  X  X  0  X  0  X  X  0  0  X  0  0  0  X  X  0  0  X  X  0  0  X  0  0  X  0  0
 0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  X  X  0  X  0  X  0  0  0  0  0  X  0  X  0  0  X  0  0  X  X  0  X  0  0  X  0  X  0  0  0  0  X  0  X  X  0  X  X  0  0  X  0  X  X  0  0  0  0  0

generates a code of length 71 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+201x^56+494x^60+22x^62+705x^64+330x^66+1253x^68+924x^70+1548x^72+660x^74+1009x^76+110x^78+516x^80+2x^82+303x^84+98x^88+13x^92+2x^96+1x^120

The gray image is a linear code over GF(2) with n=142, k=13 and d=56.
This code was found by Heurico 1.16 in 34.3 seconds.