The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+120x^26+407x^28+564x^30+128x^31+1065x^32+896x^33+1794x^34+896x^35+1146x^36+128x^37+578x^38+302x^40+142x^42+22x^44+2x^46+1x^60

The gray image is a code over GF(2) with n=136, k=13 and d=52.
This code was found by Heurico 1.16 in 2.24 seconds.