The generator matrix

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

generates a code of length 12 over Z2[X]/(X^4) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+106x^7+864x^8+4526x^9+20349x^10+57860x^11+94748x^12+57788x^13+20439x^14+4530x^15+803x^16+118x^17+11x^18+1x^22

The gray image is a linear code over GF(2) with n=96, k=18 and d=28.
This code was found by Heurico 1.16 in 39.8 seconds.