The generator matrix

 1  0  1  1  1 X^3+X^2+X  X  1  1 X^3+X^2  1  1  1  1 X^3 X^3+X^2+X  1  1  1 X^2+X  1  1  1 X^2+X  1  1  1  1  1  1
 0  1 X+1 X^2+X X^3+X^2+1  1  1 X^3 X^2+1  1 X^2+X+1 X^3+X^2+X X^3+X^2 X+1  1  1  0  1 X^3+X^2+X+1  1  X X^2+1 X^3  1 X^3+X^2+1 X^2+X+1 X^2+1  1 X^3+1 X+1
 0  0 X^2  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2 X^3 X^3 X^2 X^3+X^2  0 X^2 X^3  0 X^2  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3  0  0  0
 0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0 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+110x^26+208x^27+538x^28+816x^29+786x^30+816x^31+503x^32+208x^33+86x^34+12x^36+6x^38+4x^42+2x^44

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 0.109 seconds.