The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+180x^22+168x^23+663x^24+600x^25+946x^26+616x^27+555x^28+136x^29+178x^30+16x^31+28x^32+6x^34+1x^36+2x^38

The gray image is a code over GF(2) with n=208, k=12 and d=88.
This code was found by Heurico 1.16 in 0.11 seconds.