The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  1  1  1  1  1  1  1  X  1  1  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  0  X  X  0  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  0  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  0  X  X  X  0  0  X  X  0  0  0  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  0  X  X  X  X  0  0  0  X  0  0  X  X
 0  0  0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  0  0  X  X  X  0  X  0  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  0  0  X  0  0  X  X  X  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  0  0  X  0  0  X  X  0  X  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  0  X  X  0  X  X  0  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  0  X  X  X  0  X  0  0  0  X  X  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+181x^16+668x^20+1524x^24+1280x^26+5292x^28+2560x^30+3127x^32+256x^34+1172x^36+284x^40+36x^44+3x^48

The gray image is a linear code over GF(2) with n=58, k=14 and d=16.
This code was found by Heurico 1.16 in 13.8 seconds.