The generator matrix

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

generates a code of length 88 over Z4 who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+74x^71+198x^72+364x^73+543x^74+710x^75+942x^76+1168x^77+1431x^78+1784x^79+1883x^80+2206x^81+2502x^82+2874x^83+3258x^84+3258x^85+3619x^86+3774x^87+3860x^88+3734x^89+3738x^90+3700x^91+3261x^92+3026x^93+2661x^94+2316x^95+2012x^96+1656x^97+1381x^98+1078x^99+736x^100+574x^101+397x^102+268x^103+193x^104+114x^105+93x^106+50x^107+35x^108+22x^109+12x^110+8x^111+4x^112+6x^113+7x^114+4x^115+1x^120

The gray image is a code over GF(2) with n=176, k=16 and d=71.
This code was found by Heurico 1.13 in 328 seconds.