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  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2  0  0 X^3  0  0 X^3 X^3 X^3+X^2
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0
 0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3
 0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  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+19x^26+32x^27+36x^28+192x^29+544x^30+128x^31+15x^32+12x^34+32x^35+12x^36+1x^58

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.