The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  X
 0 X^3+X^2  0  0 X^3 X^3+X^2 X^3+X^2 X^2  0 X^3  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^2 X^2  0 X^2 X^3 X^3+X^2 X^2 X^3 X^3  0  0  0 X^2
 0  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3  0 X^2 X^2 X^3+X^2 X^3+X^2 X^3  0  0 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3 X^2 X^2 X^3+X^2  0 X^3+X^2 X^2 X^2 X^3+X^2
 0  0  0 X^3+X^2 X^2 X^3 X^2 X^2 X^3 X^3 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^2 X^3 X^2 X^3  0 X^3+X^2  0 X^3+X^2 X^2 X^3+X^2  0 X^3 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+50x^26+75x^28+192x^29+396x^30+192x^31+70x^32+34x^34+13x^36+1x^56

The gray image is a linear code over GF(2) with n=240, k=10 and d=104.
This code was found by Heurico 1.16 in 0.031 seconds.