The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+238x^27+726x^28+1212x^29+1857x^30+2574x^31+3434x^32+4054x^33+4183x^34+4280x^35+3791x^36+2764x^37+1761x^38+998x^39+513x^40+222x^41+101x^42+38x^43+15x^44+4x^45+2x^46

The gray image is a code over GF(2) with n=136, k=15 and d=54.
This code was found by Heurico 1.13 in 6.94 seconds.