The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1  X  0  X  1  X  X  1 X^3  1  1  X  1  X  X
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^3  0 X^2+X X^2+X X^3+X^2 X^3+X  X X^3+X^2 X^3+X^2+X  X X^3+X  X X^3+X^2+X X^2+X  0  X X^2 X^3+X X^3+X X^2+X  0 X^3
 0  0 X^3+X^2  0 X^2  0  0 X^3  0 X^2 X^2 X^2  0 X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2
 0  0  0 X^3+X^2  0  0 X^3 X^2 X^2 X^2 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^2  0 X^3 X^2 X^2 X^2 X^3  0 X^2 X^2 X^3+X^2 X^2 X^2
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0  0  0  0  0  0 X^3  0  0  0 X^3 X^3 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+231x^26+240x^27+536x^28+656x^29+868x^30+656x^31+436x^32+240x^33+159x^34+42x^36+22x^38+9x^40

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 31.6 seconds.