The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+130x^26+676x^27+1093x^28+2344x^29+3381x^30+5392x^31+6633x^32+8864x^33+8294x^34+8992x^35+6698x^36+5776x^37+3216x^38+2208x^39+1044x^40+480x^41+208x^42+76x^43+17x^44+8x^45+3x^46+2x^48

The gray image is a code over GF(2) with n=136, k=16 and d=52.
This code was found by Heurico 1.13 in 25.3 seconds.