The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+170x^31+335x^32+438x^33+478x^34+526x^35+388x^36+480x^37+384x^38+358x^39+235x^40+150x^41+90x^42+50x^43+6x^44+4x^45+3x^48

The gray image is a code over GF(2) with n=144, k=12 and d=62.
This code was found by Heurico 1.11 in 0.153 seconds.