The generator matrix

 1  0  0  0  1  1  1  1  2  1  1  X X+2  1  X  X  0  1  1  1  1  1 X+2 X+2 X+2  1  X  1  1  2  0  2  2  1
 0  1  0  0  0  1  2  3  1 X+2  3  1  1  1  2  X  1 X+3  2  X  3  0  1  1  X X+3 X+2 X+1 X+3  2  X X+2  0  3
 0  0  1  0  0  1  3  2  3  1 X+1 X+1  X X+2  1  1 X+1 X+1  X  X  X  X  0 X+2  1 X+3  X X+2  X  1  1  1  X  3
 0  0  0  1 X+1  2  1  3  3 X+2 X+3 X+2  3  2 X+1  1  2  3 X+1 X+1  X  2  3 X+2  0  2  1  3  X  2 X+2  0  1  X
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  0  0  0  2  0  2  0  0  2  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+72x^28+390x^29+526x^30+880x^31+785x^32+1018x^33+837x^34+1158x^35+802x^36+774x^37+442x^38+308x^39+99x^40+70x^41+17x^42+6x^43+4x^45+2x^46+1x^48

The gray image is a code over GF(2) with n=136, k=13 and d=56.
This code was found by Heurico 1.13 in 0.512 seconds.