The generator matrix

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

generates a code of length 22 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+28x^16+16x^17+38x^18+112x^19+242x^20+128x^21+933x^22+128x^23+226x^24+112x^25+40x^26+16x^27+14x^28+10x^30+1x^32+2x^34+1x^38

The gray image is a linear code over GF(2) with n=176, k=11 and d=64.
This code was found by Heurico 1.16 in 0.047 seconds.