The generator matrix

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

generates a code of length 86 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+189x^72+470x^74+906x^76+990x^78+1412x^80+1444x^82+1860x^84+1784x^86+1915x^88+1650x^90+1422x^92+926x^94+691x^96+336x^98+229x^100+76x^102+62x^104+4x^106+14x^108+2x^112+1x^116

The gray image is a code over GF(2) with n=172, k=14 and d=72.
This code was found by Heurico 1.16 in 60 seconds.