The generator matrix

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

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+114x^27+328x^28+618x^29+1023x^30+1336x^31+1714x^32+2038x^33+2003x^34+2032x^35+1873x^36+1366x^37+909x^38+528x^39+305x^40+138x^41+33x^42+22x^43+2x^44+1x^60

The gray image is a code over GF(2) with n=136, k=14 and d=54.
This code was found by Heurico 1.16 in 14 seconds.