The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+307x^16+117x^18+120x^20+56x^22+1128x^24+1029x^26+456x^28+4096x^29+392x^30+1303x^32+4096x^33+1346x^34+392x^36+456x^38+328x^40+538x^42+56x^44+120x^46+5x^48+41x^50+1x^58

The gray image is a linear code over GF(2) with n=62, k=14 and d=16.
This code was found by Heurico 1.16 in 8.02 seconds.