The generator matrix

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

generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+95x^20+100x^21+334x^22+388x^23+612x^24+736x^25+943x^26+1218x^27+1276x^28+1546x^29+1553x^30+1718x^31+1459x^32+1394x^33+958x^34+674x^35+567x^36+298x^37+272x^38+94x^39+80x^40+22x^41+35x^42+4x^43+6x^44+1x^46

The gray image is a linear code over GF(2) with n=60, k=14 and d=20.
This code was found by Heurico 1.16 in 20.6 seconds.