The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+53x^64+8x^65+52x^66+44x^67+124x^68+172x^69+261x^70+436x^71+522x^72+776x^73+996x^74+1176x^75+1332x^76+1504x^77+1525x^78+1472x^79+1448x^80+1152x^81+930x^82+788x^83+480x^84+436x^85+214x^86+172x^87+98x^88+48x^89+64x^90+8x^91+28x^92+26x^94+6x^96+22x^98+4x^100+5x^102+1x^110

The gray image is a code over GF(2) with n=312, k=14 and d=128.
This code was found by Heurico 1.16 in 19.5 seconds.