The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+24x^22+144x^23+254x^24+368x^25+466x^26+384x^27+256x^28+112x^29+19x^30+16x^31+1x^32+2x^34+1x^46

The gray image is a code over GF(2) with n=208, k=11 and d=88.
This code was found by Heurico 1.16 in 0.031 seconds.