The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1  X  1  1
 0  X  2 3X+2  0 3X+2  2 3X  0 3X+2  2 3X  0 3X+2 2X X+2  2 2X+2 3X 3X  2 2X 3X+2 3X+2  0  0
 0  0 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X 2X  0 2X  0 2X  0 2X 2X  0 2X  0
 0  0  0 2X  0  0 2X 2X  0 2X 2X 2X 2X  0 2X  0  0  0 2X  0 2X  0 2X 2X 2X  0
 0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  0 2X 2X 2X  0  0  0  0  0  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+32x^23+129x^24+272x^25+165x^26+240x^27+86x^28+16x^29+34x^30+16x^31+7x^32+1x^34+1x^48

The gray image is a code over GF(2) with n=208, k=10 and d=88.
This code was found by Heurico 1.16 in 0.015 seconds.