The generator matrix

 1  0  1  1  1 X+2  1  1  0  1 X+2  1  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  1  0  1  1 X+2  1  2  1  X  1  1  1 X+2  1  2  1  X  1  1  0  1 X+2  0  1  2  X  0  X  0 X+2  2  0  0  2  X X+2  X  X  0 X+2  X  0  1  1  2  2  1  1  2  0  X  X
 0  1 X+1 X+2  1  1  0 X+1  1  3  1 X+2  0 X+1  1 X+2  3  1  2 X+1  1 X+2  3  1  X  0 X+1  1 X+2  3  1 X+3  1  3  1  0 X+2 X+1  1  2  1  1  1  X X+1  1  0  1  1 X+1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  0  1  2 X+2  1  1  X  X  1  1  X X+2
 0  0  2  0  0  0  0  0  2  2  2  0  0  0  2  2  0  2  0  0  2  0  0  2  0  2  0  2  2  0  2  2  0  0  2  0  0  0  0  2  2  2  2  0  2  0  2  2  2  0  0  0  2  0  2  2  2  0  0  0  2  0  0  2  2  2  2  2  0  2  2  0  2  0  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  0  2  2  0  2  2  0  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  0  2  2  2  0  0  2  2  0  2  0  0  2  2  2  2  0  2  0  2  0  0  0  0  0  2  0  2  2  2  0  0  2  2  2  2  0  2
 0  0  0  0  2  0  0  2  2  0  2  2  0  2  0  2  0  2  0  2  2  2  2  2  0  2  2  0  2  0  2  0  2  0  2  2  0  2  0  0  0  0  2  2  2  2  2  0  2  0  0  0  2  2  0  0  0  0  2  0  0  0  2  0  2  0  0  2  0  2  2  2  0  2  2  2  0  2
 0  0  0  0  0  2  0  2  0  2  2  2  2  0  0  2  0  0  2  0  2  0  2  0  2  2  2  2  0  2  2  0  0  0  0  2  0  2  2  0  2  2  2  0  2  2  2  2  0  0  2  0  0  2  0  0  2  2  0  0  2  0  2  0  2  2  0  0  2  2  0  2  2  2  0  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  2  2  0  2  2  2  0  0  2  2  2  2  2  0  0  0  2  0  2  0  2  0  0  2  0  2  2  2  0  0  2  2  0  0  0  2  0  2  0  2  2  2  2  0  2  2  2  2  2  0  0  2  2  2  2  2  0  0  2  2  0  0  2  2  0  2  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+250x^72+282x^74+364x^76+314x^78+324x^80+286x^82+181x^84+14x^86+20x^88+5x^92+3x^96+2x^104+1x^108+1x^116

The gray image is a code over GF(2) with n=312, k=11 and d=144.
This code was found by Heurico 1.16 in 2.88 seconds.