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

generates a code of length 88 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+141x^68+437x^72+739x^76+1075x^80+256x^82+2012x^84+1792x^86+3471x^88+1792x^90+2051x^92+256x^94+1055x^96+750x^100+392x^104+126x^108+32x^112+5x^116+1x^160

The gray image is a code over GF(2) with n=176, k=14 and d=68.
This code was found by Heurico 1.16 in 91.2 seconds.