The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+214x^29+184x^30+598x^31+203x^32+798x^33+262x^34+694x^35+224x^36+498x^37+110x^38+226x^39+20x^40+26x^41+18x^42+18x^43+2x^46

The gray image is a code over GF(2) with n=136, k=12 and d=58.
This code was found by Heurico 1.16 in 2.33 seconds.