The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+273x^74+484x^76+462x^78+286x^80+220x^82+134x^84+82x^86+45x^88+35x^90+9x^92+16x^94+1x^100

The gray image is a code over GF(2) with n=316, k=11 and d=148.
This code was found by Heurico 1.16 in 1.34 seconds.