The generator matrix

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

generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+135x^16+102x^18+767x^20+1144x^22+3399x^24+4486x^26+6659x^28+5536x^30+5386x^32+2642x^34+1741x^36+424x^38+293x^40+2x^42+49x^44+2x^48

The gray image is a linear code over GF(2) with n=58, k=15 and d=16.
This code was found by Heurico 1.16 in 21.6 seconds.