The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1  0  1  1  1  2  1  X X+2  1  1  1  1  X  X  1  1  X  X  1  1  0
 0  1  1  0  1  1  X X+3  1 X+2  1 X+3  0  1 X+1  3  2  1  0  1  1 X+1  2  1  X  1  1 X+3  X  X X+2  X X+2  1
 0  0  X  0  0  0  0  0  0  2  2  X  X  X  0 X+2  X X+2 X+2 X+2  2 X+2  0  2 X+2 X+2  X X+2  2  0  X  2 X+2 X+2
 0  0  0  X  0  0  X  2  X  2 X+2  0  0  0 X+2 X+2 X+2 X+2  X  2  X  0  2  X  2 X+2  X  2 X+2 X+2  X  2  2  2
 0  0  0  0  X  0  0  X  2  2  0  2 X+2  X X+2  2 X+2  X  0  2 X+2 X+2 X+2  2  0  2  0  X  X X+2  X  2  X X+2
 0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  2  2  2  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  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+72x^27+169x^28+310x^29+452x^30+626x^31+939x^32+1036x^33+993x^34+1078x^35+960x^36+620x^37+403x^38+254x^39+128x^40+76x^41+39x^42+18x^43+11x^44+6x^45+1x^46

The gray image is a code over GF(2) with n=136, k=13 and d=54.
This code was found by Heurico 1.16 in 9.96 seconds.