The generator matrix

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

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+244x^27+745x^28+772x^29+888x^30+572x^31+475x^32+204x^33+112x^34+64x^35+17x^36+2x^40

The gray image is a linear code over GF(2) with n=240, k=12 and d=108.
This code was found by Heurico 1.16 in 0.063 seconds.