The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+81x^44+96x^45+72x^46+3x^48+3x^60

The gray image is a code over GF(2) with n=180, k=8 and d=88.
This code was found by Heurico 1.16 in 0.0324 seconds.