The generator matrix

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

generates a code of length 20 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+125x^16+124x^17+480x^18+648x^19+1356x^20+640x^21+480x^22+120x^23+100x^24+4x^25+16x^26+2x^32

The gray image is a linear code over GF(2) with n=160, k=12 and d=64.
This code was found by Heurico 1.16 in 0.078 seconds.