The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+23x^74+36x^75+50x^76+94x^77+113x^78+92x^79+43x^80+32x^81+21x^82+2x^84+2x^85+2x^86+1x^150

The gray image is a code over GF(2) with n=312, k=9 and d=148.
This code was found by Heurico 1.16 in 0.254 seconds.