The generator matrix

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

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+195x^74+293x^76+197x^78+160x^80+83x^82+53x^84+31x^86+1x^88+2x^90+2x^92+2x^104+4x^106

The gray image is a code over GF(2) with n=312, k=10 and d=148.
This code was found by Heurico 1.16 in 18.8 seconds.