The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  1 X^2  1  1  X  1  1  1  1  1 X^2
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2  0 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^2 X^2 X^3 X^3 X^2 X^2 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^2 X^3  0 X^3+X^2 X^2 X^3+X^2 X^2  0  0 X^3+X^2  0 X^2  0 X^3 X^3+X^2
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3  0  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 26.

Homogenous weight enumerator: w(x)=1x^0+158x^26+259x^28+256x^29+742x^30+256x^31+246x^32+90x^34+4x^36+34x^38+1x^44+1x^48

The gray image is a linear code over GF(2) with n=240, k=11 and d=104.
This code was found by Heurico 1.16 in 96.9 seconds.