The generator matrix

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

generates a code of length 26 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+234x^21+1557x^22+3554x^23+7797x^24+12094x^25+14734x^26+12526x^27+8052x^28+3302x^29+1321x^30+270x^31+68x^32+18x^33+4x^34+2x^35+2x^36

The gray image is a code over GF(2) with n=208, k=16 and d=84.
This code was found by Heurico 1.16 in 11.5 seconds.