The generator matrix

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

generates a code of length 26 over Z2[X]/(X^4) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+118x^22+192x^23+540x^24+848x^25+792x^26+816x^27+458x^28+176x^29+102x^30+16x^31+23x^32+12x^34+2x^36

The gray image is a linear code over GF(2) with n=208, k=12 and d=88.
This code was found by Heurico 1.16 in 0.078 seconds.