The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+47x^34+10x^35+103x^36+58x^37+230x^38+148x^39+437x^40+248x^41+942x^42+348x^43+1325x^44+412x^45+1333x^46+368x^47+937x^48+248x^49+427x^50+138x^51+209x^52+58x^53+64x^54+12x^55+47x^56+24x^58+11x^60+5x^62+2x^64

The gray image is a code over GF(2) with n=180, k=13 and d=68.
This code was found by Heurico 1.16 in 3.61 seconds.