The generator matrix

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

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+127x^28+160x^30+32x^31+345x^32+224x^33+318x^34+224x^35+316x^36+32x^37+134x^38+91x^40+26x^42+13x^44+2x^46+2x^48+1x^56

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 0.157 seconds.