The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+152x^20+904x^21+3023x^22+7588x^23+15096x^24+23972x^25+28946x^26+24910x^27+15302x^28+7288x^29+2763x^30+824x^31+232x^32+44x^33+20x^34+6x^35+1x^40

The gray image is a code over GF(2) with n=208, k=17 and d=80.
This code was found by Heurico 1.16 in 41.6 seconds.