The generator matrix

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

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+38x^25+72x^26+92x^27+292x^28+134x^29+826x^30+138x^31+274x^32+68x^33+52x^34+24x^35+8x^36+14x^37+10x^38+2x^39+2x^41+1x^48

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 2.42 seconds.