The generator matrix

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

generates a code of length 44 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+21x^40+44x^41+33x^42+34x^43+33x^44+30x^45+22x^46+12x^47+7x^48+1x^50+1x^52+2x^53+4x^54+1x^56+4x^57+4x^58+2x^59

The gray image is a code over GF(2) with n=88, k=8 and d=40.
This code was found by Heurico 1.16 in 0.015 seconds.