The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+32x^34+66x^35+167x^36+236x^37+452x^38+612x^39+971x^40+1286x^41+1542x^42+1912x^43+1837x^44+1892x^45+1635x^46+1260x^47+947x^48+632x^49+388x^50+230x^51+153x^52+48x^53+39x^54+16x^55+17x^56+2x^57+6x^58+3x^60+1x^62+1x^70

The gray image is a code over GF(2) with n=176, k=14 and d=68.
This code was found by Heurico 1.16 in 8.52 seconds.