The generator matrix

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

generates a code of length 29 over Z2[X]/(X^4) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+112x^22+764x^23+2391x^24+6628x^25+15856x^26+29576x^27+47974x^28+54790x^29+48674x^30+30294x^31+15701x^32+6144x^33+2196x^34+772x^35+198x^36+54x^37+10x^38+2x^39+7x^40

The gray image is a linear code over GF(2) with n=232, k=18 and d=88.
This code was found by Heurico 1.16 in 180 seconds.