The generator matrix

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

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+320x^74+426x^76+404x^78+362x^80+234x^82+119x^84+86x^86+47x^88+26x^90+3x^92+10x^94+2x^96+4x^98+4x^102

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 15.8 seconds.