The generator matrix

 1  0  1  1  1  X  1  1 X^3+X^2+X  1  1 X^2+X  1  1 X^3+X^2  1  1  1 X^3+X^2  1  1  1  0  1  0  1 X^2  X  1  1
 0  1  1 X^2 X+1  1  X X^3+1  1  0 X^3+1  1 X^3+X^2+X X^2+X+1  1 X^2+X X^2+X+1 X^3+X^2  1 X^2 X^2+1  X  1 X^2+1  1 X^3+X^2 X^2 X^3 X^3+X^2+X X^2+X
 0  0  X X^3+X X^3 X^3+X X^3+X X^3 X^3+X^2+X X^3+X^2 X^2+X  0 X^2  X X^3+X^2+X X^3+X^2+X X^2+X X^3+X^2+X X^3 X^3+X^2  0 X^3+X^2  X X^3+X^2 X^2  0  X X^3+X  X  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+142x^27+320x^28+424x^29+432x^30+288x^31+225x^32+148x^33+32x^34+18x^35+12x^36+4x^37+2x^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 0.266 seconds.