The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+256x^78+58x^80+292x^82+20x^84+162x^86+34x^88+84x^90+4x^92+64x^94+9x^96+18x^98+12x^102+2x^104+6x^106+2x^110

The gray image is a code over GF(2) with n=168, k=10 and d=78.
This code was found by Heurico 1.16 in 75.5 seconds.