The generator matrix

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

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+23x^26+40x^27+24x^28+464x^29+36x^30+328x^31+27x^32+32x^33+4x^34+32x^35+12x^36+1x^58

The gray image is a linear code over GF(2) with n=240, k=10 and d=104.
This code was found by Heurico 1.16 in 0.016 seconds.