The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  X  1  X  1  1  X  0  X  1  X  1  X  1  X
 0  X  0  0  0  X X+2  X  2  2  0  0  X  X  X X+2  0  0  X  X  X  2 X+2 X+2  2  2  X  2 X+2  X  0  2  0  0
 0  0  X  0  X  X  X  0  2  0  X X+2 X+2  0 X+2  0  2 X+2  0  2  0 X+2 X+2  2  2  2  X  2  0  2  X  0 X+2  0
 0  0  0  X  X  0  X X+2  0  X  X  2  2 X+2  X  0  2  X  X X+2 X+2  0 X+2  2 X+2 X+2 X+2 X+2  X X+2  0  X  0  0
 0  0  0  0  2  0  0  0  2  2  2  0  2  2  0  2  2  0  2  2  2  2  2  2  2  0  0  2  2  0  2  2  2  2
 0  0  0  0  0  2  0  2  0  0  2  2  0  0  2  0  2  2  2  0  2  0  0  0  2  0  0  0  2  2  2  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+84x^28+16x^29+245x^30+80x^31+299x^32+160x^33+348x^34+160x^35+269x^36+80x^37+156x^38+16x^39+75x^40+48x^42+7x^44+3x^46+1x^48

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 0.145 seconds.