The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X X^2  1  X  1  X  1  1
 0  2  0  0  0  0  0  0  0  0  2  2  0  0  0  2  0  0  2  2  0  2  2  2  2  0
 0  0  2  0  0  0  0  0  0  2  2  2  0  2  2  0  0  2  2  0  0  2  2  2  0  2
 0  0  0  2  0  0  0  0  0  2  0  2  2  2  0  2  2  2  0  0  0  0  2  0  2  0
 0  0  0  0  2  0  0  0  2  0  0  2  2  0  2  2  0  2  0  2  0  2  0  2  0  0
 0  0  0  0  0  2  0  0  2  0  2  0  0  2  2  2  2  2  0  0  0  0  2  2  2  2
 0  0  0  0  0  0  2  0  2  2  2  0  0  0  2  2  2  2  2  2  2  2  2  0  0  2
 0  0  0  0  0  0  0  2  2  2  0  0  2  2  2  0  2  0  2  0  2  0  0  0  0  2

generates a code of length 26 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+58x^20+32x^22+146x^24+256x^25+1088x^26+256x^27+120x^28+32x^30+43x^32+14x^36+2x^40

The gray image is a code over GF(2) with n=208, k=11 and d=80.
This code was found by Heurico 1.16 in 0.188 seconds.