The generator matrix

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

generates a code of length 44 over Z4 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+75x^34+138x^35+224x^36+304x^37+392x^38+438x^39+463x^40+550x^41+542x^42+574x^43+602x^44+662x^45+680x^46+630x^47+521x^48+402x^49+337x^50+240x^51+150x^52+114x^53+72x^54+28x^55+23x^56+16x^57+13x^58+1x^74

The gray image is a code over GF(2) with n=88, k=13 and d=34.
This code was found by Heurico 1.16 in 5.45 seconds.