The generator matrix

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

generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+116x^20+248x^24+160x^26+541x^28+320x^30+440x^32+32x^34+150x^36+30x^40+9x^44+1x^48

The gray image is a linear code over GF(2) with n=58, k=11 and d=20.
This code was found by Heurico 1.16 in 0.25 seconds.