The generator matrix

 1  0  0  1  1  1 X+2  1  1  2 X+2  1  1  X  0 X+2  1  1 X+2  X  1  0  1  2  1  1  1  1  1  1  2  1  X  1
 0  1  0  0  1 X+1  1  2  3  1  0  X X+1  1  1 X+2  1  0  X  1  2  0  3  1 X+3 X+2 X+2 X+2 X+1 X+3  1  0 X+2 X+3
 0  0  1  1  1  0  1 X+2  X X+3  1  1  1 X+2  X  1  3 X+3  1 X+3 X+2  1 X+1 X+2  1  3  0  3  X  X  0 X+1  1  0
 0  0  0  X X+2  0  X X+2 X+2  2 X+2  2 X+2  2  X  0  0  0  X  0  0  X  X  2  2  X  X  2  X  X  2 X+2  2  2
 0  0  0  0  2  0  2  0  0  2  0  0  0  2  2  2  2  2  2  0  0  2  0  2  2  2  2  0  2  2  0  2  2  0
 0  0  0  0  0  2  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  0  0  2  2  0  2  2  0  2  0  2  0  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+152x^28+308x^29+598x^30+712x^31+763x^32+980x^33+1066x^34+1120x^35+892x^36+716x^37+410x^38+216x^39+156x^40+44x^41+38x^42+20x^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 1.48 seconds.