The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+87x^34+158x^35+303x^36+412x^37+637x^38+678x^39+812x^40+944x^41+977x^42+1152x^43+1192x^44+1394x^45+1310x^46+1230x^47+1157x^48+1108x^49+808x^50+638x^51+517x^52+316x^53+251x^54+106x^55+100x^56+44x^57+23x^58+4x^59+12x^60+6x^61+2x^62+2x^63+2x^64+1x^66

The gray image is a code over GF(2) with n=90, k=14 and d=34.
This code was found by Heurico 1.16 in 42.3 seconds.