The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+168x^28+260x^29+548x^30+800x^31+876x^32+948x^33+962x^34+1104x^35+867x^36+732x^37+464x^38+208x^39+155x^40+44x^41+42x^42+13x^44

The gray image is a code over GF(2) with n=136, k=13 and d=56.
This code was found by Heurico 1.16 in 1.47 seconds.