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

generates a code of length 87 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+173x^68+534x^72+846x^76+1207x^80+384x^82+2308x^84+2432x^86+3635x^88+1152x^90+1529x^92+128x^94+973x^96+698x^100+299x^104+77x^108+6x^112+1x^116+1x^160

The gray image is a code over GF(2) with n=174, k=14 and d=68.
This code was found by Heurico 1.16 in 91.6 seconds.