The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  0  1  1  1  1  1  1  1  1  1  1  X  X  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^3+X^2 X^2+X  0 X^3+X X^3 X^2+X X^3+X X^2+X  X  0 X^3+X^2 X^3+X^2+X  0 X^3 X^2+X X^3+X^2+X X^2 X^3+X^2 X^3+X^2 X^2+X X^2+X  0
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3
 0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0

generates a code of length 30 over Z2[X]/(X^4) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+30x^25+65x^26+142x^27+67x^28+404x^29+643x^30+404x^31+54x^32+142x^33+55x^34+30x^35+4x^36+5x^38+1x^40+1x^52

The gray image is a linear code over GF(2) with n=240, k=11 and d=100.
This code was found by Heurico 1.16 in 0.047 seconds.