The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  1  1  0 X^2+X  1  1  1  1 X^3+X^2 X^3+X  1  1  1  1  X  X
 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^2+X X+1 X^2+1  1  1 X^3+X^2 X^3+X X+1 X^2+1  1  1  0 X^3 X^3+X  X X^3+X^2+X  X
 0  0 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 X^3 X^3  0  0 X^3 X^3  0  0  0  0
 0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 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 28.

Homogenous weight enumerator: w(x)=1x^0+338x^28+368x^30+293x^32+16x^34+6x^36+2x^40

The gray image is a linear code over GF(2) with n=240, k=10 and d=112.
This code was found by Heurico 1.16 in 9.78 seconds.