The generator matrix

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

generates a code of length 30 over Z2[X]/(X^4) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+188x^27+268x^28+416x^29+380x^30+368x^31+216x^32+152x^33+28x^34+20x^35+2x^36+8x^37+1x^40

The gray image is a linear code over GF(2) with n=240, k=11 and d=108.
This code was found by Heurico 1.16 in 0.359 seconds.