The generator matrix

 1  0  1  1 X^2+X  1  1  1  0  1  1  X  1  1 X^3+X  1  1 X^3+X^2  0  1 X^3+X^2+X X^3+X^2 X^3  0  X  1  X  1  1  1
 0  1  1 X^2+X  1 X^3+X+1 X^3+X^2+1 X^2  1  X X^3+X^2+X+1  1 X^2  1  1 X^2+X+1 X^3+X  1  1 X^2+X+1  1  X  1  1  1 X^3  0  X X^3+X^2  0
 0  0  X  0 X^3 X^2 X^3+X^2 X^3+X X^3+X^2+X  X X^3+X^2+X X^3+X X^3+X^2+X X^2+X X^2+X  X X^3+X^2+X X^3+X^2+X X^3 X^2 X^3+X^2+X X^3+X X^2  X X^3+X^2 X^2 X^3+X X^3+X^2 X^3  0
 0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0  0  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  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+74x^26+340x^27+537x^28+834x^29+667x^30+824x^31+365x^32+260x^33+121x^34+36x^35+17x^36+10x^37+9x^38+1x^42

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 0.094 seconds.