The generator matrix

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

generates a code of length 44 over Z4 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+54x^35+131x^36+154x^37+218x^38+242x^39+257x^40+270x^41+267x^42+304x^43+314x^44+304x^45+303x^46+288x^47+231x^48+240x^49+194x^50+122x^51+71x^52+54x^53+36x^54+14x^55+15x^56+2x^57+3x^58+4x^60+3x^62

The gray image is a code over GF(2) with n=88, k=12 and d=35.
This code was found by Heurico 1.16 in 1.58 seconds.