The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+84x^34+150x^35+244x^36+284x^37+342x^38+396x^39+489x^40+572x^41+551x^42+646x^43+606x^44+642x^45+639x^46+570x^47+529x^48+442x^49+350x^50+252x^51+146x^52+106x^53+74x^54+34x^55+29x^56+2x^57+6x^58+4x^60+1x^62+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 5.58 seconds.