The generator matrix

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

generates a code of length 88 over Z4 who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+44x^75+110x^76+176x^77+222x^78+278x^79+305x^80+366x^81+446x^82+418x^83+371x^84+424x^85+413x^86+382x^87+430x^88+404x^89+453x^90+414x^91+378x^92+358x^93+302x^94+322x^95+276x^96+230x^97+194x^98+148x^99+87x^100+74x^101+71x^102+32x^103+20x^104+14x^105+11x^106+8x^107+6x^108+2x^111+2x^113

The gray image is a code over GF(2) with n=176, k=13 and d=75.
This code was found by Heurico 1.10 in 5.29 seconds.