The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  X  X  X  1  1
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  0  X  X  0  X  0  0  X  X  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  0  X  0  0  0  0  X  X  0  0  0  X
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  0  X  X  X  X  0  0  0  X  0  X
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  X  0  X  X  X  0  X  X  X  X
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  X  0  X  X  X  X  0  X  X  X  0  X  0
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  X  X  0  0  X  0  X  X  0  X  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  X  X  X  0  0  0  X  0  X  X  X
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  X  0  X  0  X  0  0  0  0  0  X

generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+42x^22+73x^24+140x^26+134x^28+216x^30+230x^32+76x^34+56x^36+30x^38+15x^40+8x^42+2x^44+1x^48

The gray image is a linear code over GF(2) with n=60, k=10 and d=22.
This code was found by Heurico 1.16 in 30.1 seconds.