The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1  2 X+2 X+2 X+2  1  1  X  X  0  2  1 X+2  1  1  1 X+2  1  1  1  1  1  1
 0  1  0  0  0  1  3  1  2  2 X+3  3  1  1 X+2  1  2  X  X  1 X+2 X+2  1  1  2  0 X+3  1  X X+2 X+2 X+3 X+2  2
 0  0  1  0  1  1  2  3 X+2  3 X+1  2 X+1 X+2  1  2 X+1 X+2  1  0  2  1  0 X+3 X+1 X+2 X+1 X+1  3  2  1  X  3  2
 0  0  0  1  1  2  1  1  3  X  3  0  X  3 X+3  1  0 X+1  1  X  1  2  0  3 X+3 X+1  3  2 X+2  3 X+1  X  0  2
 0  0  0  0  X  0  0  0  0  2  2  2  2  2  2 X+2 X+2 X+2 X+2  X X+2  X X+2  X  0  X  X  X X+2  0  X  0  0  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+86x^27+330x^28+626x^29+979x^30+1290x^31+1664x^32+2136x^33+2210x^34+1994x^35+1788x^36+1454x^37+911x^38+462x^39+233x^40+116x^41+60x^42+24x^43+16x^44+4x^45

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 4.93 seconds.