The generator matrix

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

generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+34x^19+99x^20+250x^21+413x^22+548x^23+725x^24+956x^25+1177x^26+1398x^27+1654x^28+1688x^29+1665x^30+1564x^31+1283x^32+1020x^33+740x^34+498x^35+301x^36+174x^37+97x^38+48x^39+31x^40+8x^41+3x^42+6x^43+2x^44+1x^46

The gray image is a linear code over GF(2) with n=58, k=14 and d=19.
This code was found by Heurico 1.16 in 21.5 seconds.