The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+154x^16+294x^20+128x^22+1064x^24+768x^26+1126x^28+128x^30+301x^32+114x^36+16x^40+2x^44

The gray image is a linear code over GF(2) with n=52, k=12 and d=16.
This code was found by Heurico 1.16 in 0.654 seconds.