The generator matrix

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

generates a code of length 88 over Z4 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+218x^78+379x^80+468x^82+514x^84+428x^86+416x^88+362x^90+334x^92+298x^94+285x^96+156x^98+107x^100+62x^102+39x^104+18x^106+5x^108+6x^110

The gray image is a code over GF(2) with n=176, k=12 and d=78.
This code was found by Heurico 1.16 in 47.3 seconds.