The generator matrix

 1  0  1  1  1  0  1  1  0  1  X  1  1  1 X+2  1  X  1  1  1  1  0 X+2  1  2  1  1  X  1  1  0  0  2  1
 0  1  1  0  1  1  2 X+1  1 X+2  1  1  1  2  1 X+1  1  2 X+3  2  3  1  1 X+1  0  X  2  1 X+2 X+2  X  1  1  0
 0  0  X  0  0  0  0  0  0  0  0  2  X X+2 X+2  X  X  X  X  2 X+2 X+2  X  2  2 X+2  2  X  X X+2  0  X  0  X
 0  0  0  X  0  0  0  0  X X+2 X+2 X+2  X  X  0 X+2  X  2  X  0  X  0  2 X+2  2  0  2  2 X+2 X+2  2 X+2 X+2  X
 0  0  0  0  X  0  2 X+2  0  2  0  X  2 X+2 X+2  2 X+2  X  0  2  2  X  X X+2  X X+2  2 X+2 X+2  0  X  2  2  0
 0  0  0  0  0  X X+2 X+2 X+2  X  2  X  X  2  0  0  2  X  X X+2  0 X+2  2  0 X+2  2 X+2  X  2  X  0  X X+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+73x^26+158x^27+340x^28+530x^29+863x^30+1300x^31+1724x^32+2082x^33+2191x^34+2128x^35+1737x^36+1366x^37+873x^38+476x^39+287x^40+118x^41+92x^42+34x^43+7x^44+3x^46+1x^62

The gray image is a code over GF(2) with n=136, k=14 and d=52.
This code was found by Heurico 1.16 in 6.29 seconds.