The generator matrix

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

generates a code of length 24 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+76x^20+460x^21+1231x^22+1136x^23+2450x^24+1180x^25+1091x^26+396x^27+128x^28+24x^29+13x^30+4x^31+1x^32+1x^34

The gray image is a linear code over GF(2) with n=192, k=13 and d=80.
This code was found by Heurico 1.16 in 0.375 seconds.