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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+37x^66+4x^67+120x^68+12x^69+272x^70+120x^71+586x^72+412x^73+1005x^74+764x^75+1380x^76+1112x^77+1758x^78+1296x^79+1770x^80+1112x^81+1364x^82+764x^83+982x^84+412x^85+541x^86+120x^87+225x^88+12x^89+97x^90+4x^91+21x^92+32x^94+23x^96+9x^98+8x^100+5x^102+3x^104+1x^108

The gray image is a code over GF(2) with n=316, k=14 and d=132.
This code was found by Heurico 1.16 in 19.7 seconds.