The generator matrix

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

generates a code of length 29 over Z2[X]/(X^4) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+56x^23+1190x^24+2826x^25+8342x^26+15204x^27+23994x^28+27308x^29+24734x^30+15392x^31+8273x^32+2492x^33+962x^34+196x^35+78x^36+12x^37+10x^38+2x^41

The gray image is a linear code over GF(2) with n=232, k=17 and d=92.
This code was found by Heurico 1.16 in 47.2 seconds.