The generator matrix

1 0 0 0 0 0 1 1 1 2 0 0 2 1 1 2 2 1 1 1 2 1 1 1 1 1 0 0 2 0 1 1 1 2 0 0 1 2 0 2 1 2 1 1 1
0 1 0 0 0 0 0 0 0 0 1 2 1 1 1 1 1 2 3 0 1 0 1 1 3 1 1 2 0 2 3 3 1 1 1 0 2 1 1 2 2 0 0 2 0
0 0 1 0 0 0 0 0 0 0 0 1 3 1 2 3 1 1 2 3 2 1 0 2 1 0 1 1 1 0 0 2 2 3 0 2 2 1 3 1 3 1 1 1 0
0 0 0 1 0 0 0 1 1 1 2 0 1 0 2 0 3 3 1 2 0 2 1 0 1 3 3 1 3 1 0 2 3 0 2 0 1 2 3 3 3 2 0 0 0
0 0 0 0 1 0 1 0 1 3 2 0 3 0 1 1 2 3 3 3 3 3 0 0 2 0 2 3 0 1 2 1 0 2 0 2 1 2 0 0 3 0 0 2 0
0 0 0 0 0 1 1 3 2 1 1 1 2 3 2 0 0 3 3 1 1 0 3 1 0 0 3 2 2 2 0 0 0 1 2 1 0 3 3 1 0 0 2 0 0
0 0 0 0 0 0 2 2 0 2 2 2 0 2 0 2 2 0 0 0 2 2 0 0 0 2 0 2 0 0 2 2 0 2 0 0 2 0 0 0 2 2 0 0 0

generates a code of length 45 over Z4 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+18x^34+80x^35+173x^36+262x^37+291x^38+326x^39+401x^40+540x^41+543x^42+526x^43+600x^44+626x^45+648x^46+582x^47+575x^48+494x^49+416x^50+326x^51+237x^52+224x^53+115x^54+76x^55+55x^56+30x^57+15x^58+4x^59+6x^60+2x^62

The gray image is a code over GF(2) with n=90, k=13 and d=34.
This code was found by Heurico 1.10 in 2.2 seconds.