The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1 X^2  1  X  1  1  X  1  1  X X^3
 0  X  0  X X^3  0 X^2+X X^2+X X^2 X^2 X^3+X^2+X  X X^3+X^2 X^3+X X^3+X^2+X X^2+X X^3+X^2+X X^2 X^2  X X^3+X^2 X^3+X  X X^3+X^2 X^3+X^2 X^2 X^3+X X^3+X^2 X^3 X^2
 0  0  X  X X^2 X^2+X X^2+X  0 X^3+X^2  X X^2 X^3+X^2+X X^3 X^3+X^2+X X^2 X^2+X X^3+X X^2+X  X X^2+X  X X^2 X^3+X X^3+X^2+X  0 X^3+X^2+X X^3+X^2 X^3+X^2 X^3+X^2+X  X
 0  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3  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+252x^27+102x^28+692x^29+64x^30+620x^31+78x^32+168x^33+52x^35+10x^36+4x^37+4x^39+1x^48

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 12 seconds.