The generator matrix

1 0 0 0 0 0 0 1 1 1 0 1 1 X 1 1 0 0 X 1 1 0 1 1 X 1 X X 1 1
0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 X+1 X 1 X 1 X X 1 X 1 1 X 1 0 0
0 0 1 0 0 0 0 0 1 1 X 0 X+1 1 X X+1 1 X+1 1 X X 1 X+1 0 X 1 X X+1 1 0
0 0 0 1 0 0 0 1 0 X+1 1 X 0 0 1 1 0 X X+1 X 1 1 X 0 0 1 0 X+1 1 0
0 0 0 0 1 0 0 1 X 0 1 X+1 X+1 1 X+1 0 X 0 X+1 X 1 0 X X+1 X X 0 X 0 0
0 0 0 0 0 1 0 1 X+1 X X X+1 X 1 0 1 X+1 0 X 1 X 0 0 X X+1 X 1 0 X 0
0 0 0 0 0 0 1 X X 1 1 X+1 1 1 1 1 X+1 1 0 0 X+1 1 X 1 1 0 1 X+1 X 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+80x^20+110x^21+357x^22+396x^23+585x^24+680x^25+1004x^26+1202x^27+1256x^28+1680x^29+1550x^30+1644x^31+1359x^32+1348x^33+1034x^34+744x^35+594x^36+258x^37+251x^38+104x^39+87x^40+20x^41+26x^42+6x^43+6x^44+2x^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 1.10 in 3.56 seconds.