The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  0  1  X  1  1  1  1  1  1  1  1  1  1 X^3  1 X^2+X  1  0  X  1  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3+X+1 X^3+X^2  1 X^2+1  1 X^2+X X^3 X+1 X^2+X X+1 X^2  0  X X^3+X^2+1  1  1  X  1  1  1  1 X^3+1 X^3+X^2+1 X^3
 0  0 X^2  0  0 X^3  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3 X^3 X^2 X^3 X^3+X^2  0 X^3+X^2  0
 0  0  0 X^3+X^2 X^3 X^2 X^2  0 X^2 X^3+X^2 X^3 X^2  0 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3  0 X^2 X^3 X^3+X^2 X^3  0 X^2 X^3+X^2  0  0 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+80x^26+194x^27+803x^28+398x^29+1204x^30+372x^31+771x^32+172x^33+64x^34+10x^35+8x^36+6x^37+12x^38+1x^44

The gray image is a linear code over GF(2) with n=240, k=12 and d=104.
This code was found by Heurico 1.16 in 0.109 seconds.