The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+31x^14+152x^16+262x^18+246x^20+330x^22+512x^23+598x^24+1536x^25+790x^26+1536x^27+662x^28+512x^29+368x^30+263x^32+226x^34+114x^36+38x^38+10x^40+2x^42+2x^44+1x^46

The gray image is a linear code over GF(2) with n=52, k=13 and d=14.
This code was found by Heurico 1.16 in 3.28 seconds.