The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+376x^72+684x^74+948x^76+636x^78+540x^80+284x^82+332x^84+164x^86+88x^88+24x^90+16x^92+3x^96

The gray image is a code over GF(2) with n=312, k=12 and d=144.
This code was found by Heurico 1.16 in 1.28 seconds.