The generator matrix

1 0 0 0 0 0 1 1 1 X 0 0 0 0 1 1 1 X 0 X 1 1 1 1 1 0 1 1 0 1 1 X X 1 X 0 1 1 X 1 X 1 0 X 1 1 1 1 X X 1 0 X 1 1 1 0 0 0 X 1 1 1 1 1 1 1 1 1
0 1 0 0 0 0 0 0 0 0 1 X 1 1 0 X+1 X X 1 1 1 0 X+1 X+1 X 0 1 1 1 X+1 X X 1 1 X X X X+1 1 0 1 X 1 1 X X+1 X+1 X 0 0 1 1 1 1 0 X 0 1 0 1 1 1 X+1 X 1 1 0 X+1 1
0 0 1 0 0 0 0 0 0 0 X 1 1 X+1 X+1 1 1 1 1 X 1 X+1 X 1 X+1 1 0 X 1 1 1 X 0 0 1 1 0 1 X+1 X+1 X 1 1 0 X 1 X+1 0 0 X X 0 1 X+1 X+1 1 1 X+1 X X 0 0 0 0 1 0 X+1 X+1 X+1
0 0 0 1 0 0 0 1 1 1 1 1 0 1 X 0 X+1 1 X 0 X 1 1 X+1 0 X X+1 X 1 1 0 1 1 0 X+1 X X+1 X+1 X X X+1 X 1 1 0 X 0 X+1 X X X+1 X X X X+1 1 X 1 X X+1 0 1 X 0 1 X X+1 X X
0 0 0 0 1 0 1 0 X+1 1 1 1 X X+1 1 1 X X X+1 1 0 X+1 0 X+1 0 X+1 1 X X 0 1 X+1 X X+1 X+1 X+1 0 0 1 X+1 1 X+1 0 0 1 1 X 0 1 1 X+1 0 1 0 1 1 X X 0 X 0 X X X+1 X+1 1 X+1 1 1
0 0 0 0 0 1 1 X+1 X 1 0 X 1 X+1 X X+1 0 X+1 0 X+1 0 1 0 X 1 X+1 X+1 1 0 1 0 X+1 X+1 0 0 X+1 1 X+1 0 X X X+1 X+1 X X 0 X+1 X X+1 1 X 1 1 X+1 0 1 X X+1 1 0 0 1 X 1 X 0 0 X+1 0
0 0 0 0 0 0 X X 0 0 0 0 0 0 X X X 0 0 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 0 X X X 0 X 0 0 0 X X X X X X 0 X 0 0 X X 0 0 X 0 0 0 0 X X X 0

generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+200x^58+513x^60+731x^62+845x^64+939x^66+958x^68+891x^70+911x^72+816x^74+628x^76+422x^78+208x^80+88x^82+25x^84+8x^86+6x^88+1x^90+1x^96

The gray image is a linear code over GF(2) with n=138, k=13 and d=58.
This code was found by Heurico 1.10 in 3.33 seconds.