The generator matrix

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

generates a code of length 87 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+108x^72+48x^74+430x^76+282x^78+773x^80+582x^82+1002x^84+832x^86+1109x^88+764x^90+876x^92+410x^94+504x^96+142x^98+188x^100+12x^102+91x^104+30x^108+6x^112+2x^116

The gray image is a code over GF(2) with n=174, k=13 and d=72.
This code was found by Heurico 1.16 in 18.3 seconds.