The generator matrix

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

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+196x^26+244x^27+432x^28+796x^29+854x^30+784x^31+348x^32+192x^33+176x^34+28x^35+32x^36+4x^37+6x^38+2x^40+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 27.8 seconds.