The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1  0  1  1  X  1 X^3+X^2  1  X  X  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^3+X^2 X^3+X^2 X^3+X^2+X+1  1 X^3+X  0 X^3+X X^3
 0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0
 0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 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+21x^26+172x^27+258x^28+392x^29+365x^30+448x^31+211x^32+120x^33+26x^34+20x^35+10x^36+3x^38+1x^50

The gray image is a linear code over GF(2) with n=240, k=11 and d=104.
This code was found by Heurico 1.16 in 0.031 seconds.