The generator matrix

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

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+82x^29+134x^30+214x^31+168x^32+356x^33+195x^34+352x^35+136x^36+196x^37+106x^38+64x^39+14x^40+4x^41+12x^42+8x^43+2x^45+2x^47+1x^48+1x^50

The gray image is a code over GF(2) with n=136, k=11 and d=58.
This code was found by Heurico 1.16 in 1.72 seconds.