The generator matrix

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

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+19x^20+136x^21+168x^22+600x^23+211x^24+600x^25+149x^26+136x^27+23x^28+2x^30+1x^32+1x^34+1x^40

The gray image is a linear code over GF(2) with n=192, k=11 and d=80.
This code was found by Heurico 1.16 in 0.031 seconds.