The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+244x^39+442x^40+692x^41+698x^42+946x^43+667x^44+1010x^45+765x^46+794x^47+557x^48+588x^49+334x^50+262x^51+91x^52+58x^53+25x^54+10x^55+2x^56+4x^57+2x^58

The gray image is a code over GF(2) with n=180, k=13 and d=78.
This code was found by Heurico 1.16 in 84 seconds.