The generator matrix

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

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+82x^27+384x^28+518x^29+1122x^30+1192x^31+1806x^32+1786x^33+2453x^34+1860x^35+2067x^36+1166x^37+1057x^38+424x^39+277x^40+110x^41+39x^42+26x^43+9x^44+4x^45+1x^46

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 4.55 seconds.