The generator matrix

 1  0  0  1  1  1 X^2  0 X^3 X^2  1  1  1 X^3+X  1  1  X  1  1  X X^3+X^2+X  1  1 X^2  1 X^3  1 X^3+X  1  1
 0  1  0  0 X^3+X^2+1  1  1 X^2+X  1  1 X^3 X^3+X^2+1 X^3+1 X^3+X X^3 X^2+X+1  1 X^2+X X+1  1 X^3+X^2 X+1 X^3+X^2+X X^2 X^2+X+1  1 X^2 X^2+X X+1 X^2
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^3+X^2+X  1 X^3+X^2+X  1 X^3+X  1 X^3+X^2+1 X^2+X+1 X^3+1 X+1 X^3+X^2+X X^3+X^2+X+1  1 X^3  X  1 X^3+X X^2+X+1  0  1 X^3+X+1  0
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  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+79x^26+642x^27+1149x^28+1670x^29+1478x^30+1446x^31+853x^32+578x^33+184x^34+72x^35+29x^36+8x^37+2x^38+1x^42

The gray image is a linear code over GF(2) with n=240, k=13 and d=104.
This code was found by Heurico 1.16 in 0.859 seconds.