The generator matrix

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

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+516x^26+1016x^27+2224x^28+2784x^29+3376x^30+2928x^31+2007x^32+928x^33+500x^34+24x^35+56x^36+24x^38

The gray image is a linear code over GF(2) with n=240, k=14 and d=104.
This code was found by Heurico 1.16 in 128 seconds.