The generator matrix

 1  0  1  1  1 X+2  1  1 X+2  1  1  0  1  1  2  1  1  X  1  1  X  1  1  2  1  1  0  1  1 X+2  1  1  1  1  0 X+2  1  1  1  1  2  X  1  1  1  1  2  X  X  X  0  X  X  2  X  X  0  X  X X+2 X+2  1  2  1  1  1  X  X  1  1  X  X  1  1  1  X  1  1
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  2 X+3  1  X  1  1  0 X+1  1 X+2  3  1  0 X+2 X+1  3  1  1  2  X X+3  1  1  1  2  X X+3  1  1  1  0 X+2  X  2  X  X  0 X+2  X  2  X  1  1  0  X  0  2  2  1  1 X+1 X+1  X X+2 X+3 X+3  3 X+2  3  1
 0  0  2  2  0  2  2  0  0  0  2  2  2  2  2  0  0  0  0  0  2  2  2  0  0  0  2  2  2  0  2  0  2  0  0  2  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  2  2  2  0  0  0  0  0  0  2  0  0  2  2  0  2  0  0  2  2  2  2  0  0  0  2  2

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+24x^77+78x^78+15x^80+4x^81+2x^86+4x^89

The gray image is a code over GF(2) with n=312, k=7 and d=154.
This code was found by Heurico 1.16 in 0.236 seconds.