The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+120x^27+494x^28+1408x^29+2490x^30+4492x^31+7156x^32+10224x^33+13686x^34+16340x^35+17655x^36+16638x^37+14005x^38+10618x^39+7305x^40+4278x^41+2237x^42+1162x^43+407x^44+218x^45+93x^46+34x^47+6x^48+2x^49+1x^50+2x^51

The gray image is a code over GF(2) with n=144, k=17 and d=54.
This code was found by Heurico 1.13 in 99.4 seconds.