The generator matrix

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

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+125x^22+40x^23+232x^24+344x^25+610x^26+344x^27+200x^28+40x^29+57x^30+44x^32+8x^34+2x^36+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 5.34 seconds.