The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  X  1  1  1  0  1  1  0  0  0  1  0  1  1  1
 0  1  0  0  0  1  1  1  0  X X+1 X+1  1  1  0  1  0  0  1  X  1  0  0  0  1  1  1  1  X  0
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  1  1 X+1  1 X+1  1  0  X  0  1  0  X  X  1 X+1  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  0  1  X  1  0  X  X X+1  X  1 X+1  0 X+1  1  0 X+1  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  0  X  X  X  X  0  X  X  0  X  X  0  X  0  X  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  X  0  X  X  X  0  0  X  0  X  0  0  X  X  0  X  0
 0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  X  X  0  0  0  0  X  0  0  X  0  X  0  X  0
 0  0  0  0  0  0  0  X  0  X  0  0  X  0  X  0  X  X  0  0  X  X  0  X  0  0  X  0  X  0
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  X  X  X  0  X  X  X  0  0  0  0  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+40x^20+68x^21+166x^22+176x^23+287x^24+392x^25+447x^26+600x^27+684x^28+746x^29+812x^30+872x^31+737x^32+664x^33+486x^34+360x^35+240x^36+160x^37+118x^38+40x^39+55x^40+16x^41+19x^42+4x^44+2x^45

The gray image is a linear code over GF(2) with n=60, k=13 and d=20.
This code was found by Heurico 1.16 in 2.66 seconds.