The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  1  1  0  1  1  1  X  X  1  X  0  1  1
 0  1  0  0  0  1  1  1  X  0 X+1 X+1  1  1  X  1  1  0  X  0  0  1  1  0 X+1  1  1  1  1
 0  0  1  0  1  1  0  1  0 X+1 X+1  X  X X+1  1  1  X X+1  X  X  1  0  0  1 X+1  1  0  1  1
 0  0  0  1  1  0  1  1  1  0  1  X X+1  0  1 X+1  1 X+1  1  0  X  0  0 X+1  X  1 X+1  X  1
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  0  X  X
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  X  X  0  X  0  X  X  0  0  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  0  0  X  0  X  0  X
 0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  0  0  0  X  0  0  0  0  X  X  0  X  X

generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+40x^21+132x^22+168x^23+203x^24+236x^25+348x^26+368x^27+293x^28+404x^29+440x^30+376x^31+313x^32+308x^33+208x^34+96x^35+74x^36+36x^37+20x^38+16x^39+11x^40+4x^42+1x^44

The gray image is a linear code over GF(2) with n=58, k=12 and d=21.
This code was found by Heurico 1.16 in 0.892 seconds.