The generator matrix

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

generates a code of length 88 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+89x^72+32x^74+331x^76+212x^78+688x^80+448x^82+926x^84+872x^86+1124x^88+768x^90+926x^92+516x^94+597x^96+192x^98+266x^100+32x^102+119x^104+43x^108+6x^112+4x^116

The gray image is a code over GF(2) with n=176, k=13 and d=72.
This code was found by Heurico 1.16 in 18.3 seconds.