The generator matrix

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

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+133x^22+228x^23+290x^24+416x^25+513x^26+546x^27+666x^28+782x^29+860x^30+814x^31+728x^32+638x^33+504x^34+402x^35+276x^36+158x^37+95x^38+54x^39+20x^40+10x^41+7x^42+4x^43+2x^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 1.16 in 2.95 seconds.