The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  2  1  2  1  1  2  2  2  1  2  1  2  1  1  2  2  1  2  1  2  2  2  2  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  2  2  2  2  2  0  0  2  0  2  2  2  0  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  2  0  2  2  0  2  2  0  0  2  2  2  2  0  2  2  0  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  0  0  2  0  2  2  0  2  0  2  2  2  0  2  2  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  0  0  2  2  2  2  2  0  0  0  0  0  0  0  2  2  0  2  2  0  0  0  2  0  2  2  2  2  0  0  2  2  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  0  0  2  0  2  2  0  2  2  0  2  2  2  0  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  2  2  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  2  0  0  2  0  2  0  0  2  0  2  0  0  2  0  0  0  2  0  2  2  2  0  0  2  0  2  2  2  0  0  2  2  0  0  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  2  2  0  0  0  2  2  0  2  0  0  2  2  2  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  0  2  2  2  0  2  0  2  2  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  0  2  0  0  2  2  0  0  0  2  2  2  0  2  0  2  0  2  2  2  0  2  0  2  2  0  0  0  0  2  2  0  2  0  2  2  0  2  2  2  0  2  2  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  2  0  0  2  0  0  2  0  2  0  2  0  2  0  2  2  2  2  0  0  2  0  0  0  2  0  2  0  2  2  2  0  0  0  2  2  2  2  0  2  2  0  0  2  2  2  0  2  0
 0  0  0  0  0  0  0  0  0  0  2  0  0  2  0  2  0  2  0  0  0  2  2  0  0  2  0  2  0  2  0  0  2  2  0  2  2  2  0  0  2  2  0  0  0  2  2  0  0  2  2  2  2  2  2  0  2  0  0  0  2  0
 0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  0  2  0  2  2  2  0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  0  0  2  2  2  0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  2  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  0  2  2  2  2  0  0  2  0  0  2  2  2  2  2  0  2  0  2  0  0  2  2  2  2  0  0  0  2  0  2  0  2  2  2  0  2  2  2  0  2  0  0  0  0  0

generates a code of length 62 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+64x^44+127x^46+208x^48+2x^49+325x^50+38x^51+427x^52+98x^53+488x^54+336x^55+602x^56+774x^57+689x^58+1222x^59+710x^60+1646x^61+795x^62+1616x^63+785x^64+1182x^65+778x^66+786x^67+636x^68+366x^69+482x^70+96x^71+394x^72+26x^73+294x^74+2x^75+202x^76+2x^77+83x^78+54x^80+25x^82+9x^84+6x^86+4x^88+1x^90+3x^94

The gray image is a code over GF(2) with n=124, k=14 and d=44.
This code was found by Heurico 1.16 in 54.1 seconds.