The generator matrix

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

generates a code of length 30 over Z2[X]/(X^4) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+288x^26+32x^27+700x^28+448x^29+1154x^30+544x^31+634x^32+244x^34+40x^36+10x^38+1x^48

The gray image is a linear code over GF(2) with n=240, k=12 and d=104.
This code was found by Heurico 1.16 in 35.7 seconds.