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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+66x^28+39x^30+118x^32+40x^33+81x^34+120x^35+103x^36+200x^37+107x^38+280x^39+106x^40+248x^41+122x^42+104x^43+80x^44+24x^45+90x^46+8x^47+31x^48+53x^50+7x^52+19x^54+1x^62

The gray image is a linear code over GF(2) with n=78, k=11 and d=28.
This code was found by Heurico 1.16 in 0.416 seconds.