The generator matrix

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

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+87x^22+16x^23+423x^24+240x^25+576x^26+240x^27+324x^28+16x^29+100x^30+19x^32+4x^34+1x^38+1x^40

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 0.047 seconds.