The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+183x^72+24x^73+82x^74+104x^75+210x^76+240x^77+62x^78+304x^79+167x^80+216x^81+40x^82+104x^83+113x^84+32x^85+48x^86+69x^88+22x^90+20x^92+2x^94+4x^96+1x^132

The gray image is a code over GF(2) with n=316, k=11 and d=144.
This code was found by Heurico 1.16 in 0.746 seconds.