The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  0  1  1  1 X+2  1  1  1 X+2  1  1  1  0  0  1 X+2  1  1  1  2  X
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0  1 X+1 X+2  3  1  0  3 X+2  1  0  3 X+1  1  1 X+1  1 X+2  3  3  X  0
 0  0  2  0  0  0  0  0  0  2  2  0  2  0  0  0  2  2  2  2  0  2  0  0  2  0  2  2  2  2  2  2  0  0
 0  0  0  2  0  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  2  2  2  0  0  2  2  2  0  0
 0  0  0  0  2  0  0  0  2  0  2  0  2  2  2  2  2  0  2  0  0  2  2  0  0  0  0  2  0  2  0  2  0  0
 0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  2  0  2  0  2  2  0  0  0  2  2  0  2  0  2  2  2  0  0
 0  0  0  0  0  0  2  2  0  2  0  2  2  2  2  2  2  2  2  0  2  0  0  0  2  0  2  0  0  0  0  2  2  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+78x^28+24x^29+169x^30+88x^31+293x^32+144x^33+424x^34+144x^35+358x^36+88x^37+156x^38+24x^39+34x^40+16x^42+4x^44+1x^46+2x^54

The gray image is a code over GF(2) with n=136, k=11 and d=56.
This code was found by Heurico 1.16 in 0.106 seconds.