The generator matrix

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

generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+44x^21+135x^22+216x^23+299x^24+430x^25+476x^26+568x^27+716x^28+750x^29+818x^30+830x^31+734x^32+626x^33+532x^34+382x^35+272x^36+190x^37+79x^38+50x^39+21x^40+8x^41+8x^42+2x^43+4x^44+1x^48

The gray image is a linear code over GF(2) with n=60, k=13 and d=21.
This code was found by Heurico 1.10 in 1 seconds.