The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+60x^19+175x^20+388x^21+615x^22+952x^23+1539x^24+2148x^25+2981x^26+3908x^27+4746x^28+5654x^29+6237x^30+6502x^31+6345x^32+5660x^33+4974x^34+3952x^35+2867x^36+2228x^37+1533x^38+928x^39+547x^40+288x^41+165x^42+80x^43+36x^44+18x^45+7x^46+2x^47

The gray image is a linear code over GF(2) with n=62, k=16 and d=19.
This code was found by Heurico 1.11 in 60.1 seconds.